Question

Perpendicular drawn from the centre to a chord bisects the chord

Answer 1

✯✯ QUESTION ✯✯

Perpendicular drawn from the centre to a chord bisects the chord..

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✰✰ ANSWER ✰✰

☛Let a Circle with centre O. AB is chord and OC perpendicular to AB..

➮To Prove : -

• AC = BC

➮Construction : -

• Join OA and OB

➮Proof : -

✔In Δ OCA and Δ OCB : -

$\implies\tt{OA=OB}$ (Radius)

$\implies\tt{\angle{OCA}=\angle{OCB}}$ (Each 90°)

$\implies\tt{OC=OC}$ (Common)

☛So , By RHS rule Δ OCA ≅ Δ OCB....

➥Now ,

$\implies\tt{AC=BC}$ (By CPCT Rule)

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★RHS Rule : -

Right Angle Hypotoneus Side.

If in two right Triangle the hypotenuse and one side of one triangle are equal to the hypotenuse and one side of other triangle then the two sides are congruent..

★CPCT means Corresponding Parts of Congruent Triangle.

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