Circle and Triangle Question... (A triangle is inside of a circle)

Question

A circle has a diameter AC of 10 inches. The chord AB is 8 inches long. What is the area of the region outside the triangle but inside the circle? (Triangle ABC is a right triangle.)

 

Please show all the steps involved in solving the problem. The π symbol is pi.

The following choices are provided as answers:

 

A.) 25π-24 square inches

B.) 100π-24 square inches

C.) 25π-40 square inches

D.) 100π-40 square inches

Answer 1

There are a few facts that make this "V-8" problem.

1. Because AB is a diameter of the circle, any triangle formed by adding a third vertex B that also lies along the circle will be a right triangle, with AB its hypotenuse and <B a right angle.
2. Because ABC is a right triangle, BC can be deduced to be 6 inches. 6-8-10 is a Pythagorean triple.

 

Then you calculate:

1. The area of the triangle is 24 sq in
2. You know the diameter of the circle is 10 inches. Its area is therefore 25π.

 

The answer is therefore A) 25π-24 sq in.