Question

Prove that a diameter ab of a circle bisectsall those cords which are parallel to tangent at pt a

Answer 1

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Here we have a circle with centre at Oand diameter AOB with a line l as tangent to the circle at A. Let us consider a chord CD||l cutting AOB at Q. As CD||l, it isapparent that CD⊥l.
Now in ΔsCOQand OQD,we have

OC=OD →both are radius of same circle

∠OQC=∠OQD=90∘ as CD||L

OQ=OQ →being common to two triangles

Hence using RHS, we have
ΔCOQ≡ΔOQDand hence CQ=DQ

i.e. AB bisects CD

See the diagram in picture

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