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Question
Using ruler and a compass only construct a semi-circle with diameter BC = 7cm. 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.
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Solution
- Draw a line segment BC = 7 cm.
- Taking the midpoint of BC as centre O, draw a semicircle.
with radius = 3.5 cm. - Now, the semicircle circumscribes the ΔABC.
- Draw angle bisector of ∠ABC and make it intersect the
semi-circle at D. - Measure the angle ∠DBC, which comes out to be 22.5°
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