Question

In figure given, M is the midpoint of QR. ZPRO = 90°. Prove that, PQ2 = 4PM2 - 3PR2 ​

Answer 1

Answer:

PQ² = 4PM²-3PR²

Step-by-step explanation:

According to Pythagoras theorem,

In APRM,

P * R ^ 2 + R * M ^ 2 = P * M ^ 2

RM²= PM² - PR2 ....(1)

In APRQ,

P * R ^ 2 + R * Q ^ 2 = P * Q ^ 2

=>PQ² = PR² + (RM + MQ)²

=>PQ² = PR² + (RM + RM)²

=>PQ² = PR² + (2RM)²

=>PQ² = PR² + 4RM²

=>PQ² = PR² + 4(PM² - PR2).--------.(from 1)

→ PQ2 = PR2 + 4PM² - 4PR²

PQ² = 4PM²-3PR²

Hence, P * Q ^ 2 = 4P * M ^ 2 - 3P * R ^ 2