Question

line RS is tangent at point Q . if pqs =65° find m (arc pmq) and(arc pnq)
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Answer 1

Given :- line RS is tangent at point Q . ∠PQS = 65° .

To Find :- find m(arc PMQ) and (arc PNQ) ?

Solution :-

Construction :- Let O is the centre of the circle . Join OQ and OP .

so,

→ OQ = OP { Radius. }

→ OQ ⟂ RS { Radius is perpendicular to tangent. }

now,

→ ∠OQP = ∠OQS - ∠PQS = 90° - 65° = 25° .

so,

→ ∠OQP = ∠OPQ = 25° { since OQ = OP .}

then, in ∆QOP,

→ ∠OQP + ∠OPQ + ∠POQ = 180° { By angle sum property. }

→ 25° + 25° + ∠POQ = 180°

→ ∠POQ = 180° - 50°

→ ∠POQ = 130° .

therefore,

→ m(arc PMQ) = 130°

→ m(arc PNQ) = 360° - m(arc PMQ) = 360° - 130° = 260° .

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