Question

In the given figure, O is the Centre of a circle. If the length of chord PQ is equal to the radius of the circle, then PRQ is
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Answer 1

Given :- In the given figure, O is the Centre of a circle. If the length of chord PQ is equal to the radius of the circle .

To Find :-

• ∠PRQ = ?

Solution :-

In ∆POQ, we have,

→ PO = QO { Radius of circle. }

also,

→ PQ = radius (given)

so,

→ PO = QO = PQ

then, ∆POQ will be a an equaliteral ∆ . { since all sides are equal.}

therefore,

→ ∠POQ = 60° { Each angle in an equaliteral ∆ is equal to 60°.}

hence,

→ ∠PRQ = (1/2)∠POQ { Angle at Circumference is half of angle at centre .}

→ ∠PRQ = (1/2) * 60° = 30° (Ans.)

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