Q17 of 100 Page 17

In Fig. 16.188, ABCD is a cyclic quadrilateral. Find the value of x.

∠FDC + ∠CDA = 180^o (Linear pair)

80^o + ∠CDA = 180^o

∠CDA = 100^o

Since, ABCD is a cyclic quadrilateral

∠ADC + ∠ABC = 180^o

100^o + ∠ABC = 180^o

∠ABC = 80^o

Now,

∠ABC + ∠ABF = 180^o (Linear pair)

80^o + x = 180^o

x = 180^o – 80^o

= 100^o

In Fig. 16.187, ∠BAD=78°, ∠DCF=x° and ∠DEF=y°. Find the values of x and y.

In a cyclic quadrilateral ABCD, if ∠A-∠C=60°, prove that the smaller of two is 60°.

ABCD is a cyclic quadrilateral in which:

(i) BC||AD, ∠ADC=110° and ∠BAC=50°. Find ∠DAC.

(ii) ∠DBC=80° and ∠BAC=40° Find ∠BCD.

(iii) ∠BCD=100° and ∠ABD=70°. Find ∠ADB.

Prove that the perpendicular bisectors of the sides of a cyclic quadrilateral are concurrent.