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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 \angleACB.

Solution :

             

In \triangleOAB,

               OA = AB        (Given )

              OA = OB          (Radii of circle)

So,  OA=OB=AB

\Rightarrow ABC is a equilateral triangle.

So,\angleAOB = 60 \degree

  \angleAOB  = 2 \angleADB 

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

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

ACBD is a cyclic quadrilateral .

So, \angleACB+\angleADB =180 \degree

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

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

 

 

 

 

 

 

 

 

 

 

 

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