Q29 of 100 Page 17

In Fig. 16.189, ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If ∠DBC=55° and ∠BAC=45°, find ∠BCD.

Since angles on the same segment of a circle are equal

Therefore,


∠CAD = ∠DBC = 55o


∠DAB = ∠CAD + ∠BAC


= 55o + 45o


= 100o


But,


∠DAB + ∠BCD = 180o (Opposite angles of a cyclic quadrilateral)


Therefore,


∠BCD = 180o – 100o


∠BCD = 80o


More from this chapter

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ABCD is a cyclic trapezium with AD||BC. If ∠B=70°, determine other three angles of the trapezium.

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Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

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In Fig. 16.193, two circles intersect at A and B. The centre of the smaller circle is O and it lies on the circumference of the larger circle. If ∠APB=70°, find ∠ACB.

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In Fig. 16.194, two congruent circles with centres O and O’ intersect at A and B. If ∠AO’B=50°, then find ∠APB.