Question

Using ruler and a compass only construct a semi-circle with diameter BC = 7 cm. Locate a point A on the circumference of the semicircle such that A is equidistant from B and C. Complete the cyclic quadrilateral ABCD, such that D is equidistant from AB and BC. Measure ∠ADC and write it down.

Answer 1

Steps of Construction : 

1. Draw a line segment BC = 7 cm. 

2. Draw its perpendicular bisector 1 and let it intersect BC in M. 

3. With M as centre and radius equal to BM or CM, draw a semi-circle and let the semi-circle intersect the perpendicular bisector of line segment BC in A. Join BA. 

4. Draw the angle bisector of ∠ABC and let it intersect the semi-circle in D. 

5. Join AD and CD.

Hence, ∠ADC = 135°