Question

In the given circle, O is the centre and P is the mid-point of its chord AB. Prove that OP is perpendicular to AB.​

Answer 1

Answer:

In △s OAP and OBP,

OP=OP (Common)

OA=OB (Radius of circle)

PA=PB (Given)

Thus, △OPA≅△OPB (SAS rule)

Hence, ∠OPA=∠OPB=x (By cpct)

Sum of angles, ∠OPA+∠OPB=180

o

(Angles on a straight line)

x+x=180

o

x=90

∘

Thus, ∠OPA=∠OPB=90

∘

OP is perpendicular to AB.

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