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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 :

  1. Draw a line segment BC = 7 cm.

  2. Create a semicircle with BC as diameter.

  3. Make right bisector of BC and construct perpendicular from it such that it meets the semicircle at A as shown in figure.

  4. Construct angle bisector of ∠ABC, and let it meet the semicircle at point D.

  5. Join the points to form quadrilateral ABCD.

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, ML Aggarwal Understanding Mathematics Solutions ICSE Class 10.

On, measuring we get ∠ADC = 135°.

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