Cool Geometry

Geometry Level 3

Two tangents are drawn to a circle from an exterior point A. They touch the circle at points B and C, respectively. A third tangent intersects segments AB at P and AC at R. If AB = 20.15 cm, what is the perimeter of the triangle APR?

The answer is 40.3.

1 solution

Brian Charlesworth
Aug 18, 2015

Let $Q$ be the point where the third tangent touches the circle. Now, using the fact that the two tangents from a point to a circle have the same length, we note that

$|AC| = |AB|, |RQ| = |RC|$ and $|PQ| = |PB|.$

Thus $|AR| + |RQ| = |AR| + |RC| = |AC| = |AB|,$ and

$|AP| + |PQ| = |AP| + |PB| = |AB|.$

So the perimeter of $\Delta APR = |AR| + |RQ| + |AP| + |PQ| = 2|AB| = \boxed{40.3}.$

Cool Geometry

The answer is 40.3.

1 solution

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