The lengths of tangents from two given points to a given circle are $t_{1} & t_{2}$ . If the two points are conjugate to each other w.r.to the given circle the distance between the points will be

\sqrt{\frac{t_{1}^{2} + t_{2}^{2}}{2}}

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\sqrt{t_{1}^{2} + t_{2}^{2}}

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\sqrt{t_{1} t_{2}}

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\frac{2 t_{1} t_{2}}{t_{1} + t_{2}}

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Solution

The correct option is B $\sqrt{t_{1}^{2} + t_{2}^{2}}$
Let P and Q be the conjugate points and O be the center.

Since P, Q are conjugate

$⟹ P Q^{2} = O P^{2} + O Q^{2} - 2 r^{2}$

$⟹ P Q^{2} = (t_{1}^{2} + r^{2}) + (t_{2}^{2} + r^{2}) - 2 r^{2}$

$⟹ P Q^{2} = t_{1}^{2} + t_{2}^{2}$

$⟹ P Q = \sqrt{t_{1}^{2} + t_{2}^{2}}$

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The lengths of tangents from two given points to a given circle are t1&t2. If the two points are conjugate to each other w.r.to the given circle the distance between the points will be

The correct option is B √t21+t22Let P and Q be the conjugate points and O be the center. Since P, Q are conjugate ⟹PQ2=OP2+OQ2–2r2 ⟹PQ2=(t21+r2)+(t22+r2)–2r2 ⟹PQ2=t21+t22 ⟹PQ=√t21+t22

The lengths of tangents from two given points to a given circle are $t_{1} & t_{2}$ . If the two points are conjugate to each other w.r.to the given circle the distance between the points will be