Question

A circle is inscribed in a triangle PQR with PQ=10 cm, QR=8 cm and PR=12 cm and L, M and N are points on PQ, QR and PR respectively, touching the circle. Find the lengths QM, RN and PL.

Answer 1

Answer:

Step-by-step explanation:

Let PL = x

Recall that tangents drawn from an external point to a circle are equal in length.

PL = PN = x

LP=12 – x = QM

NR = 8 – x = RM

Hence QM =12 – x, MR = 8 – x,

QM + MR = QR

12 – x + 8 – x = 10

20 – 2x = 10

–2x = –10

2x = 10

\ x = 5

PL = x = 5cm

QM= 12 – x = 12 – 5 = 7cm

RN = 8 – x = 8 – 5 = 3cm

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Answer 2

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