Construct a segment of a circle on a chord of length 5cm. containing the following angles.

120°

Given an angle of 120° and chord 5cm

Rough Image :

Explanation:

x + x + 120° = 180°

[using sum of all angles in a triangle = 180°]

⇒ 2x + 120° = 180°

⇒ 2x = 180° - 120°

⇒ 2x = 60°

⇒ x = = 30°

Steps of construction:

Step 1: Draw a line segment AB = 5cm

Step 2: Draw an angle of 30° on point A and B to intersect at O.

Step 3: With centre ‘O’ and radius OA and OB, draw the circle.

Step 4: Mark a point ‘C’ under the chord AB and on the arc of the

circle . Join AC and BC.

we get M∠A0B = 240°.

Thus, ACB is the required circle segment.