ConstructionHard4 marks
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.
Topic: Loci
Previous-year question practice database
Answer
Solution diagram
Exam answer
∠ADC = 135°
Explanation
The construction places A on the perpendicular bisector of BC because AB = AC, and D on the angle bisector of ∠ABC because it is equidistant from AB and BC. Measuring the completed cyclic quadrilateral gives ∠ADC = 135°.
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