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ABCD is a cyclic quadrilateral in which AB = BC = 6 cm, O is the center of the circle and one of the diagonals of the cyclic quadrilateral passes through the center of the circle. Find the area of ΔABC.

ABCD is a cyclic quadrilateral in which AB = BC = 6 cm, O is the center of the circle and one of the diagonals of the cyclic quadrilateral passes through the center of the circle. Find the area of ΔABC. Correct Answer 18 cm<sup>2</sup>

Given:

ABCD is a cyclic quadrilateral

AB = BC = 6 cm

'O' is the center of a circle

Concept used:

The angle made in a semi-circle is 90° 

In a triangle, if two sides are equal and the angle between two sides is given, then area = 1/2 × product of two sides × sinθ

Where, θ is the angle between them, 

Calculation:

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Let us assume AC be diagonal that passes through the center

From the above figure, we can see that AC is diagonal, and then ∠ABC = 90° 

Area of triangle = (1/2) × 6 × 6 × sin90° 

⇒ 3 × 6 × 1

⇒ 18 cm2

∴ The area of ΔABC is 18 cm2 

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