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Prove that the length of the tangents dr...

Prove that the length of the tangents drawn from an external point to a circle are equal.

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Prove that the length of the tangent drawn from an external point to a circle are equal. Using the above, do the following: TP and TQ are tangents from T to the circle with circle O and R in any point on the circle. If AB is a tangent to the circle at R, prove that TA + AR =TB +BR.

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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 segments joining the points of contact at the centre.

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.