Question

In the following figure O is the centre of a
circle. If PQ and PR are chords of the
circle such that PQ = PR,OA 1 PQ and
OD L PR, then prove that AQ = DR.​

Answer 1

Given : O is the centre of a circle.

PQ and PR are chords of the circle such that PQ = PR,

OA ⊥ PQ and OD ⊥ PR

To Find : prove that AQ = DR.​

Solution:

PQ and PR are chords of the circle such that PQ = PR,

ΔOPQ & ΔOPR

OP = OP  common

PQ  = PR  given

OQ = OR  Radius

=> ΔOPQ ≅ ΔOPR

=> ∠PQO = ∠PRO  (CPCT)

=> ∠AQO = ∠DRO

in ΔOAQ & ΔODR

∠OAQ = ∠ODR = 90°

∠AQO = ∠DRO   already shown

OQ = OR  Radius

=>  ΔOAQ ≅ ΔODR   ( RHS)

=> AQ = DR

QED

Hence proved

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