Q10 of 29 Page 61

In the figure at right, AB and CD are straight lines through the centre O of a circle. If ∠AOC = 98° and ∠CDE = 35°

find (i) ∠DCE (ii) ∠ABC


According to theorem the angle subtended by a diameter on the circumference of a circle is 90°


Hence ∠CED = 90°


As the sum of all angles of a triangle CDE = 180°


∠DCE = 180 – 90 – 35 = 55°


As the sum of all angles of triangle OCB = 180°


As AB is a straight line ∠COB = 180–98 = 82°


Hence ∠ABC = 180 – 82 – 55 = 43°


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In the figure at left, PQ is a diameter of a circle with centre O. If ∠PQR = 55°, ∠SPR = 25°and ∠PQM = 50°.

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In the figure at right, ABCD is a cyclic quadrilateral whose diagonals intersect at P such that ∠DBC = 30°and ∠BAC = 50°.

Find (i) ∠BCD (ii) ∠CAD