Question

In the following, ΔPQR circumscribes the circle. If PX = 10 cm, QY = 8 cm and RZ = 6 cm, then find the perimeter of ΔPQR.

Answer 1

Given: ΔPQR circumscribes a circle; PX = 10 cm, QY = 8 cm, RZ = 6 cm.

Step-wise calculation:

1. Tangents from the same external point to a circle are equal.

Let a = PX = 10, b = QY = 8, c = RZ = 6.

2. Side lengths (each side is sum of two tangent segments from its endpoints):

QR = QX + XR

= b + c 

= 8 + 6

= 14 cm

RP = RY + YP

= c + a 

= 6 + 10

= 16 cm

PQ = PZ + ZQ

= a + b

= 10 + 8

= 18 cm

3. Perimeter = 14 + 16 + 18

= 48 cm 

The perimeter of ΔPQR is 48 cm.