MathDB

Area Ratio

Source:

December 22, 2005

geometryratiotrigonometryAMCAIMEnumber theoryrelatively prime

Problem Statement

In triangle

ABC, AB=\sqrt{30}, AC=\sqrt{6},

and

BC=\sqrt{15}.

There is a point

D

for which

\overline{AD}

bisects

\overline{BC}

and

\angle ADB

is a right angle. The ratio

\frac{\text{Area}(\triangle ADB)}{\text{Area}(\triangle ABC)}

can be written in the form

m/n,

where

m

and

n

are relatively prime positive integers. Find

m+n.

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