This is an important and exam oriented question from Chapter name- circles

Topic – Angle properties of circles

Chapter number- 15

In first qies AB is a diameter of the circle. If ∠ADC = 120°, we have to find ∠CAB.

In the figure (ii) , sides AB and DC of a cyclic quadrilateral ABCD are produced to meet at E, the sides AD and BC are produced to meet at F. x : y : z = 3 : 4 : 5, now we have to find the values of x, y and z.

ICSE Avichal publication

Understanding ICSE Mathematics

Question 8

Solution:(a) Construction: Join BC, and AC then

ABCD is a cyclic quadrilateral.

Now in ∆DCF

Ext. ∠2 = x + z

and in ∆CBE

Ext. ∠1 = x + y

Adding (i) and (ii)

x + y + x + z = ∠1 + ∠2

2 x + y + z = 180

^{o}(ABCD is a cyclic quadrilateral)

But x : y : z = 3 : 4 : 5

x/y = ¾ (y = 4/3 x)

x/z = 3/5 (z = 5/3 x.