Mathematics
The following figure shows a circle with center O. If OP is perpendicular to AB, prove that AP = BP.
Triangles
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Answer
Join OA and OB.
In △ OAP and △ OBP,
⇒ OP = OP (Common side)
⇒ OA = OB (Radius of same circle)
⇒ ∠OPA = ∠OPB (Both equal to 90°)
∴ △ OAP ≅ △ OBP (By R.H.S. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ AP = BP.
Hence, proved that AP = BP.
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