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Standard X

Mathematics

Number of Tangents Drawn from a Given Point

Draw a circle...

Question

Draw a circle with centre $O$ and radius $6$ cm. Take a point $P$ outside the circle at a distance of $10$ cm from $O$ . Draw tangents to the circle from point $P$ . Let the tangents intersect the circle in points $A$ and $B$ . Find $B P$ .

6

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8

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8.5

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None of these

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Solution

The correct option is B $8$ cm
In $△ O B P$
$(O P)^{2} = (O B)^{2} + (B P)^{2} B P = \sqrt{(O P)^{2} - (O B)^{2}} B P = \sqrt{(10)^{2} - 6^{2}} B P = \sqrt{64} = 8 c m$

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Draw a circle with centre O and radius 6 cm. Take a point P outside the circle at a distance of 10 cm from O. Draw tangents to the circle from point P. Let the tangents intersect the circle in points A and B. Find BP.

The correct option is B 8 cmIn △OBP(OP)2=(OB)2+(BP)2BP=√(OP)2−(OB)2BP=√(10)2−62BP=√64=8cm

Draw a circle with centre $O$ and radius $6$ cm. Take a point $P$ outside the circle at a distance of $10$ cm from $O$ . Draw tangents to the circle from point $P$ . Let the tangents intersect the circle in points $A$ and $B$ . Find $B P$ .

The correct option is B $8$ cm
In $△ O B P$
$(O P)^{2} = (O B)^{2} + (B P)^{2} B P = \sqrt{(O P)^{2} - (O B)^{2}} B P = \sqrt{(10)^{2} - 6^{2}} B P = \sqrt{64} = 8 c m$