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# A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

Q: 2     A chord of a circle is equal to the radius of the circle. Find the angle subtended by the chord at a point on the minor arc and also at a point on the major arc.

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Given: A chord of a circle is equal to the radius of the circle i.e. OA=OB.

To find: ADB and $\angle$ACB.

Solution :

In $\triangle$OAB,

OA = AB        (Given )

OA = OB          (Radii of circle)

So,  OA=OB=AB

$\Rightarrow$ ABC is a equilateral triangle.

So,$\angle$AOB = $60 \degree$

$\angle$AOB  = 2 $\angle$ADB

$\Rightarrow \angle ADB=\frac{1}{2}\angle AOB$

$\Rightarrow \angle ADB=\frac{1}{2}60 \degree=30$

ACBD is a cyclic quadrilateral .

So, $\angle$ACB+$\angle$ADB =$180 \degree$

$\Rightarrow \angle ACB+30 \degree= 180 \degree$

$\Rightarrow \angle ACB= 180 \degree-30 \degree=150 \degree$

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