Question

This is question for challengers

Answer 1

PQ=PR=QR=QM=RN= a. ...(Given)........ (1)

Consider ΔPMR,

QM=QR. .........[From 1]

.

. . seg PQ is the median

.

. . by Appollonius theorem,

PM²+PR²=2PQ² + 2QM²

.

. . PM² +a²=2a² +2a² .....[from 1]

PM² = 4a² - a²

PM² = 3a²

PM = √ 3a²

PM = √ 3.a

Similarly, we can prove PN = √3.a

.

. . PM=PN= √3.a