Question

The length of tangent drawn to a circle with radius r from a point P which is d units away from the centre is

Answer 1

Answer:

t=Vd^2-r^2. Answer to this question

Answer 2

Answer: The length of tangent drawn to a circle with radius r from a point P which is d units away from the centre is $\sqrt{d^{2} - r^{2} }$.

• Suppose O is the center of the circle, the tangent from point P touches the circle at point Q and the distance between P and Q be x .
• Now the line OQ and PQ will be at right angles.
• So, in triangle OQP will be a right angled triangle with right angle at OQP.
• By Pythagoras theorem, $x^{2} + r^{2} = d^{2}$.

Thus, x = $\sqrt{d^{2} - r^{2} }$.