Question

All sides of quadrilateral ABCD are tangent to circle P.

What is the perimeter of the quadrilateral below?
units

Answer 1

42 Units

Explanation:

Theorem

Tangent to a circle from the same point are equal.

Let the point of tangency be P,Q, R and S as labelled in the attached diagram.

By the above theorem,

BP=BQ=8 Units

AP=AS=4 Units

DS=DR=5 Units

CR=CQ=4 Units

Therefore:

AB=12 Units

BC=12 Units

CD=9 Units

AD=9 Units

Perimeter=12+12+9+9=42 Units