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# Challenge problems: circumscribing shapes

Solve two challenging problems that apply properties of tangents to find the perimeter of a circumscribing shape.

## Problem 1

All sides of triangle, A, B, C are tangent to circle P.
A circle centered around point P. The circle is inscribed inside triangle A B C so that each side is tangent to the circle. Side A C is fourteen units. From the tangent point on side A B to point B is sixteen units.
What is the perimeter of triangle A, B, C?
units

## Problem 2

All sides of quadrilateral A, B, C, D are tangent to circle P.
A circle centered around point P. The circle is inscribed inside quadrilateral A B C D so that each side is tangent to the circle. Side C D is twelve units. From the tangent point on side A B to point B is nine point six units. From the tangent point on side A D to point A is three point seven units.
What is the perimeter of quadrilateral A, B, C, D?
units