Q15 of 22 Page 126

O is the circumcentre of isosceles triangle ABC and ∠ABC = 120°; if the length of the radius of the circle is 5 cm, let us find the value of the side AB.

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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