Question

An abstract painting is a square of side 96 cm, and shows three circles that touch each other and the sides of the square. The top two circles have the same radius. What is the radius of the third circle?

Answer 1

27 cm

Explanation:

The right triangle shown in the diagram can be used to find the radius r. By the Pythagorean theorem, ...

24² + (72-r)² = (24+r)²

576 + 5184 -144r +r² = 576 +48r +r²

5184 = 192r

5184/192 = r = 27 . . . . cm

The radius of the third circle is 27 cm.