Thread: High School Math Problem Involving Circles, Radii and Tangent (Image Included)

originally posted by jehantry this easier solution

complete the construction by drawing BD this is perpendicular to DC.radii meet tangents at 90 deg. triangle ABX is similar to BCD. each is a right triangle with angle ABX = to BCD. corresponding angles of parallellines thereforeAB /AX=BC/1 , AX=3,AB=5 BC =5/3, AC 15/3 +5/3= 20/3=6.666

check this:

sin C = 4 / AC
or
sin C = 4 / 5 + x

also

sin C = 1 / x

4/5+x = 1/x

solve for x

x = 5/3

AC = 5 + 5/3