A geometry problem by well max

Geometry Level 3

Triangle ABC has side lengths AB = 7, BC = 9, and CA = 8. Point D is on the circumcircle of Triangle ABC such that AD bisects angle BAC. What is the value of CD/AD?

The answer is 0.6.

1 solution

Rick B
Oct 17, 2014

ABDC is a cyclic quadrilateral, so $\angle BAD = \angle BCD$ and $\angle CAD = \angle CBD$

Since $\overline{AD}$ bisects $\angle BAC$ ,

$\angle BAD = \angle CAD \implies \angle BCD = \angle CBD \implies \overline{BD} = \overline{CD}$

Let's say that $\overline{AD} = x$ and $\overline{CD} = \overline{BD} = y$ . We need to find $\frac{y}{x}$

Ptolemy's Theorem:

$9x = 15y \implies \frac{y}{x} = \frac{9}{15} = \boxed{0.6}$

A geometry problem by well max

The answer is 0.6.

1 solution

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