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Bisector and circles

Source: Kyiv City MO 2022 Round 1, Problem 9.3

January 23, 2022

geometry

Problem Statement

Let

AL

be the inner bisector of triangle

ABC

. The circle centered at

B

with radius

BL

meets the ray

AL^2 = AE\times AD

at points

L

and

E

, and the circle centered at

C

with radius

CL

meets the ray

AL

at points

L

and

D

. Show that

AL^2 = AE\times AD

.
(Proposed by Mykola Moroz)

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