Question

All sides of quadrilateral ABCD are tangent to circle P.

What is the perimeter of the quadrilateral below?
units

Answer 1

The perimeter of the quadrilateral is 42 units

Explanation:

Here, we have

For the line DC and DA are tangents to the circle then;

Distance from C to the point of contact with the circle along CD = Distance from C to the point of contact with the circle along CB = 4

Therefore;

Distance from D to the point of contact with the circle along DA is = Distance from D to the point of contact with the circle along DC = 9 - 4 = 5

Similarly, distance from A to the point of contact with the circle along AD = Distance from A to the point of contact with the circle along AB = 4

Therefore, distance from B to the point of contact with the circle along BA= 12 - 4 = 8 = Distance from B to the point of contact with the circle along BC

Hence, AB = 12

BC = 8 + 4 = 12

DC = 9

DA = 4 + 5 = 9

The perimeter of the quadrilateral = AB + BC + DC + DA = 12 + 12 + 9 + 9 = 42 units.