Multiple choice

The chord of contact of tangent from a point $P$ to a circle passes through $Q$. If ${ l }{ 1 }$ and ${ l }{ 2 }$ are the lengths of the tangents from $P$ and $Q$ to the circle, then $PQ$ is equal to $\sqrt { { { l }{ 1 } }^{ 2 }+{ { l }{ 2 } }^{ 2 } } $

  1. Assertion is true, Reason is true and reason is correct explanation for Statement-1.

  2. Assertion is true, Reason is true and Reason is NOT correct explanation for Assertion.

  3. Assertion is true, Reason is false

  4. Assertion is false, Reason is true
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A Correct answer
AI explanation

By the pole and polar relationship, if the polar of point P passes through point Q, then the polar of Q passes through P. This forms a right triangle with the center of the circle, where the lines joining the center to P and Q are perpendicular, making the angle at the center 90 degrees. Using the Pythagorean theorem on the distances from the center to P (which equals the length of the tangent l1) and the center to Q (which equals l2), the distance PQ is exactly the square root of (l1 squared plus l2 squared).

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