### One of a continuing series

Continuing into the new year, here are two easy geometry problems.

Compute the perimeters of the two shapes. Enter your answer in the comments section below.

Continuing into the new year, here are two easy geometry problems.

Compute the perimeters of the two shapes. Enter your answer in the comments section below.

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A break from geometry problems on this, the first day of 2018. Here is a short geography quiz. Following is a list of American cities, in pairs. Your job is to, for each pair, pick the city with the largest population. Some of these are easy, others not so much so. After you finish picking, post your answers in the comments section and then grade yourself by going to Wikipedia. Use the population figures from the city’s Wikipedia entry. Some cities have the same name as others in other states. Assume the most prominent in case of conflict.

- Dallas – San Diego
- Austin – San Francisco
- Philadelphia – Chicago
- Houston – Boston
- Muleshoe – Lipan (both in Texas)
- Santa Fe – Denver
- Kansas City (Kansas and Missouri)
- Topeka – Memphis
- Minneapolis – Fort Worth
- Miami – Phoenix
- Oklahoma City – Baltimore

- Yes, San Diego is more populous than Dallas. Just barely. That’s one I missed.
- In the rankings, Austin is number 11, San Francisco is number 14.
- Chicago 3, Philadelphia 5.
- Houston 4, Boston 21.
- This is an easy one. Muleshoe, Texas is much larger than Lipan.
- Denver is number 23, Santa Fe does not make the top 100.
- Kansas City, Missouri, ranks number 37. Kansas City, Kansas, does not make the list.
- Memphis is number 20, larger than Boston. Topeka does not make the list.
- Fort Worth, 17, is way ahead of Minneapolis
- Phoenix, at number 6, far out-ranks Miami.
- Baltimore 26, Oklahoma City 29.

Merry Christmas. Here is an easy one. Make the usual assumptions from the drawing. What is the value of ** x**? Post your answer as a comment below.

I expected somebody would solve this quickly, and Mike nailed it within hours of posting. Mike only provided the solution. See the comment below. Here is how it unravels. See the image.

Obviously this is a semicircle and a square with a line tangent to the circle. We now have a right triangle ABC, tangent to the circle at D.

From basic geometry we know that DB = 2. Also x = EA = AD. From there everything falls out quickly.

AB^{2}=AC^{2}+ CB^{2}

(x + 2)^{2}= (2 – x)^{2}+ 4

x = ½

See the image. The circles are radius 2.5 and 1.5. What is the area of the red section?

Post your answer as a comment below.

Two photos of the moon, taken from my house in San Antonio, Texas, two nights apart. Which photo was taken first?

No fair running to an astronomy book. No fair going outside to look at the moon. Post your answer as a comment below.

Anybody who’s spent a lot of time outdoors knows this. In the northern hemisphere, especially as far as 30° north looks up at the moon from the north. That means the terminator, the significant aspect of moon phases, moves from right to left day after day. That means that photo B was taken before photo A. In this case two days before.

Just when you thought we were finished with the math questions. This is from the Internet, so no fair running to Google for an answer.

The red right triangle is circumscribed by the large circle. The two sides of the triangle are diameters of the smaller circles. Prove the blue area is equal to the red area.

Post your answer as a comment below.

Keeping with a run of math questions… This problem is on the Internet. You have to provide an answer without going to the Internet.

The large arc is centered at O, The small arc is centered at D. Prove the two shaded areas are equal.

Post your answer as a comment below.

Mike and Steve have provided correct solutions. See the comments. Steve worked out the math, and Mike stated the path to resolution rather cryptically. Both invoked π, which is not necessary. Try this approach.

The triangle is a right, equilateral triangle. The hypotenuse is √2 times the base and is also the diameter of the small semicircle. You will have no problem from that point concluding the small semicircle’s area is ½ the area of the large semicircle. The area **A** of the small semicircle is equal to the area of the triangle + the circle segment subtended by the triangle’s hypotenuse. The area of the triangle is **A** – the area of the segment. The area of the lune outside the large semicircle is **A** – the area of the segment. Therefore the two areas are the same.

Back to math questions for a change. Full disclosure: I don’t make up all of these. This is from an Internet site. No fair going to the Internet to get the answer.

The triangle is equilateral. Prove the shaded area is equal to the inner circle. Post your answer as a comment below.

Mike is the first and only to provide the correct solution. A reasoning goes like this.

It is easy to demonstrate (exercise left to the reader) that the inner circle is ¼ the area of the outer circle. Then the region between the inner and outer circles is ¾ the area of the outer circle. The blue-shaded regions total 1/3 of this difference or ¼ the area of the outer circle. The inner circle is equal to the blue-shaded area.

More fun with word games…

37 years ago I was taking a course in database design, and the professor got onto the subject of data security. He discussed how contents of a file could be encrypted to protect your information from prying eyes. To illustrate, he wrote two lines of text on the board:

ABTAESBAD

FRSRXRMG

Then he turned to the class, pointed to the board, and asked, “What is this?”

I had been watching as he was writing and had started running some stuff through my head.

“Anybody?” the professor inquired.

I raised my hand.

He said, “Yes?”

I said, “Well the top one is a …,” and here I inserted an encryption technique. “And the second one is …,” and I mentioned another method.

The professor looked a little unsettled. “But what do these mean?”

So I told him.

Today’s question (problem) is, translate the two lines of text. Post your answer as a comment below. I will post a hint tomorrow if nobody has the solution by then.

Greg got it right. I was looking at the words. What had about that many letters? What course was I sitting in? Database Design. Bingo. Then my cruel nature emerged. The professor asked how I did that. I told him I had experience with that sort of thing, and I didn’t say any more.

Mike has pointed out the obvious. The top line of text has an extra B. My bad. I scanned this line not enough times to spot the error. I apologize for posing a Quiz Question with no answer. Here are the two lines of text that make sense.

ABTAESAD

FRSRXRMG

American Airline frequent fliers already know this one. Here are the letters:

## BBELRU

List the common English words that can be formed using all of the letters once in the word? Post your answer as a comment below.

An engineer is tasked with designing a new airplane, with two requirements. The airplane must be able to carry 8 passengers, and the design must use engine model A3-28, made by the boss’s company.

The engineer completes a design, and then does some calculations. The plane will not fly with a single engine of that model, but it will fly with two engines. The engineer’s boss tells him to modify the design and use two of the engines.

The engineer knows this is a bad idea.

Why?

Post your answer in the comments section below.

Sometimes I get these Quiz Questions where I can find them. If you flew on American Airlines recently, then you saw this one in your copy of the *American Way* magazine, courtesy of Mensa.

Enter your answer in the comments section below.

I promise, the last one of these for the next few weeks. In the meantime, here’s one more. What island is shown in the map above. Post your answer in the comments section below.

I will be done with these map Quiz Questions shortly. In the meantime, here’s another. What is the country in the map above? Post your answer in the comments section below.

I will be done with these map Quiz Questions shortly. In the meantime, here’s another. What is the country in the map above? Post your answer in the comments section below.

Continuing, another geography Quiz Question. See the map above. What does it show? Post your answer in the comments section below.

I’m taking a few days off, so here is another easy Quiz Question for the week. Name the country in the map above. Post your answer in the comments section below. John Coombes, you should be able to get this one.

All right! A number of people figured out this was on the west coast of somewhere (see the water off to the left). Helen figured it can’t be Chile or Peru. It must be Ecuador. Take note, geography students. That horizontal line running into Ecuador’s coast is the equator, after which the country is named.

Slipping back into the comfort of geography, this week’s Quiz Question tests your recollection from those lazy-crazy days when you slept through geography class in high school. Above is a piece of a map I stole off the Internet. Without rushing to Google or even a world map, what place is this?

Post your answer as a comment below.

It’s time to quit taking these Quiz Questions seriously. Here’s one for this week.

See the above photo. What is the object pictured, and what purpose did it used to serve?

Post your answers in the comments section. It’s all right to use Google to find the answer.

There’s a lot of stuff out there. Some more than others. On this planet, which is more?

- Uranium or lead
- Gold or platinum
- Sulfur or calcium
- Hydrogen or potassium
- Sodium or potassium
- Copper or zinc
- Nickel or aluminum
- Silver or nickel
- Iodine or fluorine
- Oxygen or iron

These are hard. You can use Google. Post your answers on Facebook. It’s interesting which things are more than you expected.