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Philippines Mathematical Olympiad

Geometry Difficulty 4.5 AIME Find the answer Philippines

Problem:

Triangle $ABC$ is right-angled at $C$ , and point $D$ on $AC$ is the foot of the bisector of $\angle B$ . If $AB = 6\ \mathrm{cm}$ and the area of $\triangle ABD$ is $4.5\ \mathrm{cm}^2$ , what is the length, in $\mathrm{cm}$ , of $CD$ ?

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

1.5

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