Draw a circle and a triangle as in the figure below. One vertex of the triangle is at the centre of the circle and the other two vertices are on the circle.

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Solution

The given figure shows a circle and an isosceles triangle, with two of its sides equal to the radius of the circle.

The steps of construction are as follows:

1) Draw a circle with centre O and of radius, say r units.

2) Join O with two points, say A and B on the circle. Join A and B also.

This is the required figure.

We know that triangles lying on the same base and between the same parallels are equal in area.

Here, we need to construct a triangle whose all three vertices lie on the circle and whose area is equal to the area of ΔOAB.

The steps of construction are as follows:

1) Draw a line l that is parallel to line segment AB and passes through point O.

2) Join AC and BC.

ΔABC is the required triangle whose area is equal to the area of ΔOAB.

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