Q. 15 D4.1( 9 Votes )

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Answer :

Since ∠ABC = 120° and therefore the angle subtended by arc ABC in major arc will be:

⇒ ∠APB = 180 – 120( By using Property of cyclic quadrilateral, where P is any point on circle)

⇒ ∠APB = 60°

By the theorem:-

The angle formed at the centre of a circle by an arc, is double of the angle formed by the same arc at any point on circle.

∠AOC = 2 ∠APB = 120°

In ΔAOB and ΔCOB,

AO = CO (radius)

OB = OB (given)

AB = BC (given)

∴ ΔAOB ≅ ΔCOB by SSS congruency

⇒ ∠ABO = ∠CBO = 60°

Also, ∠AOB = ∠COB = 60° .

This shows ΔOAB is an equilateral triangle.

⇒ AB = OA = 5 cm

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