Question

PQ is a diameter of circle with centre O. R is the any point on the circle seg RS bisect seg PQ. Prove that SR is the geometric mean of PS and SQ

Answer 1

Answer:

SR is the geometric mean of PS and SQ

Step-by-step explanation:

Correction :

seg RS ⊥ seg PQ

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