MathDB

2016 Geo #10

Source:

December 30, 2016

Problem Statement

The incircle of a triangle

ABC

is tangent to

BC

at

D

. Let

BC

and

\Gamma

denote the orthocenter and circumcircle of

\triangle ABC

. The

B

-mixtilinear incircle, centered at

O_B

, is tangent to lines

BA

and

BC

and internally tangent to

\Gamma

. The

C

-mixtilinear incircle, centered at

O_C

, is defined similarly. Suppose that

\overline{DH} \perp \overline{O_BO_C}

,

AB = \sqrt3

and

AC = 2

. Find

BC

.

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