Q12 of 29 Page 61

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


As ABCD is a cyclic quadrilaterals, sum of all angles = 360°


As the angle subtended by chord BC on circumference = 50°


Therefore BDC = 50°


Sum of all angles of triangle BCD = 180°


Hence BCD = 180– 30–50 = 100°


As the angle subtended by chord DC on circumference = 30°


Therefore CAD = 50°


More from this chapter

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10

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


 11

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

Find (i) ∠QPR, (ii) ∠QPM and (iii) ∠PRS.


 13

In the figure at left ,ABCD is a cyclic quadrilateral in which AB || DC. If ∠BAD = 100°

find (i) ∠BCD (ii) ∠ADC (iii) ∠ABC.


 14

In the figure at right, ABCD is a cyclic quadrilateral in which ∠BCD = 100°and ∠ABD = 50°. Find ∠ADB