Mathematics

The following figure shows a circle with center O. If OP is perpendicular to AB, prove that AP = BP.

The following figure shows a circle with center O. If OP is perpendicular to AB, prove that AP = BP. Triangles, Concise Mathematics Solutions ICSE Class 9.

Triangles

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Answer

Join OA and OB.

The following figure shows a circle with center O. If OP is perpendicular to AB, prove that AP = BP. Triangles, Concise Mathematics Solutions ICSE Class 9.

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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