In the given figure-If AC - BC- then the value of - OCB isA- 60-B- 90- 75-D- 45-

The correct option is B 90°Consider nbsp; Δ OCA and Δ OCB AC = CB (given), OA = OB (Radii of the circle) OC = OC (common side) Δ OCA≅Δ OCB nbsp;⇒∠ OCA = ...

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Byju's Answer

Standard X

Mathematics

Arc/Chord Properties of Circles

In the given ...

Question

In the given figure,If AC = BC, then the value of $∠ O C B$ is .

60°

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90°

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75°

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45°

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Solution

The correct option is B 90°
Consider $Δ O C A and Δ O C B$
AC = CB (given),
OA = OB (Radii of the circle)
OC = OC (common side)
$Δ O C A ≅ Δ O C B$
$\Rightarrow ∠ O C A = ∠ O C B$
$∠ O C A + ∠ O C B = 180^{\circ}$ ..... (Linear pair)
$2 ∠ O C B = 180^{\circ}$
$∴ ∠ O C B = 90^{\circ}$
$\Rightarrow$ A line drawn through the centre bisects the chord and is perpendicular to it.

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