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Prove that the equal chords of …

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Prove that the equal chords of a circle are equidistant from the centre of the circle

Posted by Ñoßi Ţä 4 years, 10 months ago

CBSE > Class 09 > Mathematics

2 answers

Gaurav Seth 4 years, 10 months ago

Given a circle with centre O and chords AB = CD
Draw OP⊥ AB and OQ ⊥ CD
Hence AP = BP = (1/2)AB and CQ = QD = (1/2)CD
Also ∠OPA = 90° and ∠OQC = 90°
Since AB = CD
⇒ (1/2) AB = (1/2) CD
⇒ AP = CQ
In Δ’s OPA and OQC,
∠OPA = ∠OQC = 90°
AP = CQ (proved)
OA = OC (Radii)
∴ ΔOPA ≅ ΔOQC (By RHS congruence criterion)
Hence OP = OQ (CPCT)

0Thank You

Rohit Kumar 4 years, 10 months ago

Kise birat ki bara ber jeva kendra par baraber kod antertit karti ha

0Thank You

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CBSE > Class 09 > Mathematics