Question

The vertices of a<br />triangle lie on the<br />circumference of a<br />circle. If its sides are<br />2.5 cm, 6 cm, and<br />6.5 cm, what is the<br />area of the circle (in<br />cm)?​

Answer 1

SOLUTION

GIVEN

The vertices of a triangle lie on the circumference of a circle. Its sides are 2.5 cm, 6 cm, and 6.5 cm

TO DETERMINE

The area of the circle

EVALUATION

Here it is given that the vertices of a triangle lie on the circumference of a circle. Its sides are 2.5 cm, 6 cm, and 6.5 cm

We notice from above that

$\sf{ {(2.5)}^{2} + {(6)}^{2} = {(6.5)}^{2} }$

So the given three sides form a right angle triangle with hypotenuse = 6.5 cm

Now for a right angle triangle, the hypotenuse is the diameter of the circumference of the triangle

So diameter = 6.5 cm

∴ Radius = 3.25 cm

∴ Area of the circle

= π × (3.25)² cm²

= 10.5625π cm²

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