In each of the following figures, O is the centre of the circle. Find the values of a, b and c. - Noon Academy

In each of the following figures, O is the centre of the circle. Find the values of a, b and c.

Circles | Class 10 | Exercise 17A | ICSE | Maths | Selina

In each of the following figures, O is the centre of the circle. Find the values of a, b and c.

(i)

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(A) - 5

(ii)

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(A) - 6

Solution:

(i)In the following figure,

$b\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }x\text{ }{{130}^{o}}$

[Angle at the center is double the angle at the circumference subtend by the same chord]

Hence,

$b\text{ }=\text{ }{{65}^{o}}$

Then,

$a\text{ }+\text{ }b\text{ }=\text{ }{{180}^{o~}}$

[Opposite angles of a cyclic quadrilateral are supplementary]

$a\text{ }=\text{ }{{180}^{o}}-\text{ }{{65}^{o}}~=\text{ }{{115}^{o}}$

(ii) In the following figure,

$c\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }x\text{ }Reflex\text{ }({{112}^{o}})$

[Angle at the center is double the angle at the circumference subtend by the same chord]

Hence,

$c\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }x\text{ }({{360}^{o}}-\text{ }{{112}^{o}})\text{ }=\text{ }{{124}^{o}}$

i

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