In figure, OA OD, OC OB, OD = OA and OC = OB. Prove that AB = CD – InterviewSolution

1.

In figure, OA OD, OC OB, OD = OA and OC = OB. Prove that AB = CD

Answer»

GIVEN:

$\sf{\angle DOA = \angle BOC = 90°}$

$\sf{OD = OA}$

$\sf{OC = OB}$

Proof:

Let $\sf{\angle AOC = x}$

From ∆DOC and ∆AOB,

$\sf{•\:\angle DOC = \angle AOB = 90° + x}$

$\sf{•\:OD = OA}$

$\sf{•\:OC = OB}$

By SAS CONGRUENCY,

$\bold{∆DOC \cong ∆AOB}$

By corresponding parts of congruent TRIANGLES (CPCT),

$\bold{\red{AB=CD}}$

★ HENCE proved

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