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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. - Mathematics

Sum

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

i. Draw a line segment BC = 7 cm

ii. Taking mid point of BC as centre O , draw a semi-circle
with radius = 3.5 cm

iii. Now, the semicircle circumscribes the ΔABC

iv. Draw angle bisector of ∠ABC and make it intersect the
semi-circle at D.

v. Measure the angle ∠DBC which comes out to be 22.5°

Concept: Arc and Chord Properties - Angle in a Semi-circle is a Right Angle
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