MathDB

computational, circle tangent to hypotenuse with center on right angle

Source: 2012 (-13) Swedish Mathematical Competition p3

August 31, 2020

Tangentscircleright trianglegeometry

Problem Statement

The catheti

AC

and

BC

in a right-angled triangle

ABC

have lengths

b

and

a

, respectively. A circle centered at

C

is tangent to hypotenuse

AB

at point

D

. The tangents to the circle through points

A

and

B

intersect the circle at points

E

and

F

, respectively (where

E

and

F

are both different from

D

). Express the length of the segment

EF

in terms of

a

and

b