Question

How do we draw a triangle with two of the angle 40° and 120° and circumradius 3 centimetres?

Answer 1

To construct the required triangle, we will use the following property.

Angle made by an arc at any point on the alternate arc is equal to half the angle made at the centre.

The steps of construction are as follows:

(1) Draw a circle with centre O and radius 3 cm.

(2) Take a point B on this circle and join OB.

(3) Taking O as the centre and OB as the segment, draw an angle of measure 80° such that it intersects the circle at point C.

(Since we need ∠BAC = 40° , we have drawn ∠BOC = 80°.)

(4) Taking O as the centre and OB as the segment, draw an angle of measure 240° on the other side of ∠BOC such that it intersects the circle at point A.

(Since we need ∠ACB = 120°, we have drawn ∠AOB = 240°.)

(5) Join AC, AB and BC.

ΔABC is the required triangle.