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

90°

Given an angle of 90° and chord 5cm

Steps of construction:

Rough image:

Explanation:

x + x + 90° = 180°

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

⇒ 2x + 90° = 180°

⇒ 2x = 180° - 90°

⇒ 2x = 900°

⇒ x = = 45°

Step 1: Draw a line segment AB = 5cm

Step 2: Draw an angle of 45° 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’ on the arc of the circle. Join AC and BC.

we get ∠CAB = 90°.

Thus, ACB is the required circle segment.