MathDB

Circumradius of a cyclic quadrilateral

Source: Sharygin 2019 Finals Day2 Grade 9 P1

July 31, 2019

Problem Statement

Let

R

be the circumradius of a circumscribed quadrilateral

ABCD

. Let

h_1

and

h_2

be the altitudes from

A

BC

and

CD

respectively. Similarly

h_3

and

h_4

are the altitudes from

C

AB

and

AD

. Prove that

\frac {h_1+h_2- 2R}{h_1h_2}=\frac {h_3+h_4-2R}{h_3h_4}