Question
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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Solution: let the centre of the circle be O and the two tangents forming an angle at point P from points A & B respectively
now,
we have to prove that,
now draw 2 OA & OB TO AP & BP respectively
now,
now, in quadilateral AOBP, sum of 4 angles =
as we know that,\displaystyle\angle{O}{B}{P}={90}^{\circ}&\angle{O}{A}{P}={90}^{\circ}
so,
now,
we have to prove that,
now draw 2 OA & OB TO AP & BP respectively
now,
now, in quadilateral AOBP, sum of 4 angles =
as we know that,
so,
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Question Text | 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. |
Answer Type | Text solution:1 |
Upvotes | 150 |