Long Type Questions & Answers
Mark-4
1.Prove that the angle between the two tangents drawn from an external point to a circle is
supplementary to the angle subtended by the line-segment joining the points of contact at
the centre.
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Answer:
As radius of the circle is perpendicular to the tangent.
OA⊥PA
Similarly OB⊥PB
∠OBP=90
o
∠OAP=90
o
In Quadrilateral OAPB, sum of all interior angles =360
o
⇒∠OAP+∠OBP+∠BOA+∠APB=360
o
⇒90
o
+90
o
+∠BOA+∠APB=360
o
∠BOA+∠APB=180
o
It proves the angle between the two tangents drawn from an external point to a circle supplementary to the angle subtented by the line segment
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