MathDB

VNTST 2010 Pro 2

Source:

October 24, 2010

geometrycircumcirclepower of a pointradical axisgeometry unsolved

Problem Statement

Let

ABC

be a triangle with

\widehat{BAC}\neq 90^\circ

. Let

M

be the midpoint of

BC

. We choose a variable point

D

on

AM

. Let

(O_1)

and

(O_2)

be two circle pass through

D

and tangent to

BC

at

B

and

C

. The line

BA

and

CA

intersect

(O_1),(O_2)

at

P,Q

respectively.
a) Prove that tangent line at

P

on

(O_1)

and

Q

on

(O_2)

must intersect at

S

.
b) Prove that

S

lies on a fix line.

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