Question

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.

Answer 1

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=95​180∘

∠O=100∘

∠QPR=∠P=54​100∘

Therefore ∠QPR=80∘


So,  option c is the answer.