Question

Prov that a perpendicular drawn from the centre of a circle to its chord it will bisect the chord​

Answer 1

Hello, Buddy!!

➸ STATEMENT:-

• A perpendicular drawn from the centre of a circle bisects the chord of that circle.

➸ GIVEN:-

• O is the centre of the Circle & AB is the chord.
• OP⊥AB

➸ REQUIRED TO PROVE:-

• AP = PB

➸ CONSTRUCTION:-

• Join OA & OB.

➸ REQUIRED PROOF:-

WKT

Perpendicular of a line makes two right angles at the point of intersection.

∠APO = ∠BPO → 90°

In ∆AOP & ∆BOP

OP = OP [Common Side]

∠APO = ∠BPO → 90° [OP⊥AB]

AO = BO [Radii of the same Circle]

∆APO ≅ ∆BPO (By SAS Axiom)

By CPCT

☞ AP = BP

• Hence, Proved!!

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Hope It Helps You ✌️