Question

In figure below, seg PQ is a diameter of a circle with centre O. R is any point on the

circle. seg RS ┴ seg PQ. Prove that, SR is the geometric mean of PS and SQ. [That is,

SR² = PS x SQ]​

Answer 1

Answer:

PQ is Diameter

∠PRQ = 90°

=> ∠P = 90° - ∠Q

RS ⊥ PQ

∠SRQ = 90° - ∠Q = ∠P

∠SRP = 90° - ∠P  =  ∠Q

in Δ PRS & Δ QRS

∠P = ∠SRQ

∠SRP =  ∠Q

∠S = 90°

=>  Δ PRS ≈ QRS

=> SR/SQ = PS/SR

=> SR² = PS * SQ

=>  SR is the geometric mean of PS and SQ

QED

Proved

Step-by-step explanation: