MathDB

Regional Olympiad - FBH 2009 Grade 9 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009

September 28, 2018

geometryisoscelestangentcircumcircle

Problem Statement

Let

C

be a circle with center

O

and radius

R

. From point

A

of circle

C

we construct a tangent

t

on circle

C

. We construct line

d

through point

O

whch intersects tangent

t

in point

M

and circle

C

in points

B

and

D

(

B

lies between points

O

and

M

). If

AM=R\sqrt{3}

, prove:

a)

Triangle

AMD

is isosceles

b)

Circumcenter of

AMD

lies on circle

C