Question

in the figure,O is the center of the circle angle PQR is inscribed in arc PQR and intercepts arc PXR if m(arcPXR)=80⁰ the find the angle PQR
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Answer 1

Concept:

According to angle intercept  theorem,

Angle subtended by the arc on the circumference is half of the angle of the arc.

When two angles are subtended by the same arc,

the angle at the centre of a circle is twice the

angle at the circumference.

So angle AOB = 2 × angle ACB.

Given:

O is the center of the circle angle PQR is inscribed in arc PQR and intercepts arc PXR if m(arcPXR)=80⁰

Find:

<PQR=?

Solution;

According to angle intercept  theorem,

Angle subtended by the arc on the circumference is half of the angle of the arc.

<PQR=1/2m(arcPXR)

         =1/2x80

          =40°

Hence, <PQR =40°

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