MathDB

Turkish NMO First Round - 2012 Problem - 25 {Geometry}

Source:

July 1, 2012

geometrytrigonometrycircumcircle

Problem Statement

The midpoint

M

of

[AC]

of a triangle

\triangle ABC

is between

C

and the feet

H

of the altitude from

B

. If

m(\widehat{ABH}) = m(\widehat{MBC})

,

m(\widehat{ACB}) = 15^{\circ}

, and

|HM|=2\sqrt{3}

, then

|AC|=?

<span class='latex-bold'>(A)</span>\ 6 \qquad <span class='latex-bold'>(B)</span>\ 5 \sqrt 2 \qquad <span class='latex-bold'>(C)</span>\ 8 \qquad <span class='latex-bold'>(D)</span>\ \frac{16}{\sqrt3} \qquad <span class='latex-bold'>(E)</span>\ 10

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