Find AF?

Geometry Level 3

Circle with center A and C are congruent. A,C,D are co-linear. F is a point on circle C such that GH=6 and IF=9.

If AF=x y \sqrt{y} where x and y are co-prime, find x+y.


The answer is 28.

Parallax's Den by Parallax's Den , 19, Bangladesh

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

Let the radii of the three circles be r , r , r, r, 3 r 2 \dfrac{3r}{2} and the angle ADF be α α . Then r C o s α = 15 rCosα=15 , DH = 36 =36 , DF = 54 =54 , r = √ 243 r=√243 and AF = √ 1539 = 9 √ 19 =√1539=9√19

0 Helpful 1 Interesting 0 Brilliant 1 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...