Mathematics
Using ruler and compass only, construct a semicircle with diameter BC = 7 cm. Locate a point P on the circumference of the semicircle such that A is equidistant from B and C. Completely the cyclic quadrilateral ABCD such that D is equidistant from AB and BC. Measure ∠ADC and write it down.
Locus
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Answer
Steps of construction :
Draw a line segment BC = 7 cm.
Create a semicircle with BC as diameter.
Make right bisector of BC and construct perpendicular from it such that it meets the semicircle at A as shown in figure.
Construct angle bisector of ∠ABC, and let it meet the semicircle at point D.
Join the points to form quadrilateral ABCD.
On, measuring we get ∠ADC = 135°.
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