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Question 1. If O is the centre of the circle, find the value of x in each of the following figures (using the given information):

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This is circle based question from Chapter name- circles
Topic – Angle properties of circles
Chapter number- 15

In this question we have been given the figure of circle with certain information about the angles and we have to find the value of x.

ICSE Avichal publication
Understanding ICSE Mathematics
Question no 1, exercise 15.2

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1. Solution:
From the figure
(i) ABCD is a cyclic quadrilateral

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2. Solution:

From the figure

(i) ABCD is a cyclic quadrilateral

Ext. âˆ DCE = âˆ BAD

Now arc BD subtends âˆ BOD at the center

And âˆ BAD at the remaining part of the circle.

âˆ BOD = 2 âˆ BAD = 2 x

2 x = 150oÂ (x = 750)

(ii) âˆ BCD + âˆ DCE = 180o

(Linear pair)

âˆ BCD + 800Â = 180o

âˆ BCD = 1800Â â€“ 800Â = 100o

Arc BAD subtends reflex âˆ BOD at the

Centre and âˆ BCD at the remaining part of the circle

Reflex âˆ BOD = 2 âˆ BCD

XoÂ = 2 Ã— 100oÂ = 200o

(iii) In âˆ†ACB,

âˆ CAB + âˆ ABC + âˆ ACB = 180o

(Angles of a triangle)

But
âˆ ACB = 90o

((Angles of a semicircle)

25oÂ + 90oÂ + âˆ ABC = 180o

=115oÂ + âˆ ABC = 180o

âˆ ABC = 180oÂ â€“ 1150=65o