Circles, circles, circles!

Geometry Level 2

Tangent semicircles have their diameters on the sides of a square of side length 1 1

What is the combined area of the four semicircles?

If you get your answer as π ( a − b ) \pi(a-\sqrt{b}) , Find the value of a + b a+b .


The answer is 5.

Bloons Qoth by Bloons Qoth , 21, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Nikhil N
Dec 27, 2017

Considering triangle ABC:

( 1 − r ) 2 + r 2 = ( 2 r ) 2 (1-r)^2 + r^2 = (2r)^2 (by Pythagoras' theorem)

This gives 1 − r = r ( 3 ) 1-r = r\sqrt(3)

Thus, r = ( 3 ) − 1 2 r = \frac{\sqrt(3)-1}{2} and the area of the semicircles is given by A = 4 ∗ π r 2 2 = π ( 2 − ( 3 ) ) A = 4 * \frac{\pi r^2}{2} = \pi(2-\sqrt(3))

2 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...