In the figure given below, O is the centre of the circle and triangle ABC is equilateral. Find: (i) ∠ADB, (ii) ∠AEB - Noon Academy

In the figure given below, O is the centre of the circle and triangle ABC is equilateral. Find: (i) ∠ADB, (ii) ∠AEB

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

In the figure given below, O is the centre of the circle and triangle ABC is equilateral. Find: (i) ∠ADB, (ii) ∠AEB

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(A) - 15

Selina Solutions Concise Class 10 Maths Chapter 17 ex. 17(A) - 16

Solution:

(i) According to the given question,

$\angle ACB\text{ }and\angle ADB$

are in the same segment,

So,

$\angle ADB\text{ }=\angle ACB\text{ }=\text{ }{{60}^{o}}$

(ii) Now, join

$OA\text{ }and\text{ }OB$

And,

$\angle AEB\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }Reflex\text{ }(\angle AOB)$

$=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\text{ }({{360}^{o~}}-\text{ }{{120}^{o}})\text{ }=\text{ }{{120}^{o}}$

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

i

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