Question

Prove that the line
drawn throught the centre
of a circle is bisect a chord
is perpendicular to the
chord!​

Answer 1

Answer:

The line drawn through the centre of a circle to bisect a chord is perpendicular to the chord.

Given : A chord PQ of a circle C ( O, r ) and L is the mid - point of PQ.

To prove : OL ⊥ PQ

Construction : Joint OP and OQ.

PROOF :

In ∆OLP and ∆OLQ,  

OP = OQ . (radii of same circle)

PL = QL . (given)

OL = OL . (common)

ΔOLP ≅ ΔOLQ . (SSS)  

Also,

∠OLP + ∠OLQ = 180° (linear pair)

∠OLP = ∠OLQ = 90°

Hence, OL ⊥ PQ.

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