PT and PQ are the tangents to the circle with centre C. Find the length of the tangents PT and PQ. Also, prove that (i.) angle CPT = angle CPQ and (ii.) angle PCT = angle PCQ.
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Tangent is perpendicular to radius at the point of contact.
Therefore ∠OQP=∠ORP=90∘
Sum of all the four angles of a quadrilateral is 360∘
So in quadrilateral QORP
∠PQO+∠QOR+∠ORP+∠RPQ=360∘
90∘+∠O+90∘+54∠O=360∘ [Given ∠P=54∠O]
59∠O=360∘−180∘
∠O=95180∘
∠O=100∘
∠QPR=∠P=54100∘
Therefore ∠QPR=80∘
So, option c is the answer.
Tangent is perpendicular to radius at the point of contact.
Therefore ∠OQP=∠ORP=90∘
Sum of all the four angles of a quadrilateral is 360∘
So in quadrilateral QORP
∠PQO+∠QOR+∠ORP+∠RPQ=360∘
90∘+∠O+90∘+54∠O=360∘ [Given ∠P=54∠O]
59∠O=360∘−180∘
∠O=95180∘
∠O=100∘
∠QPR=∠P=54100∘
Therefore ∠QPR=80∘
So, option c is the answer.
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