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Find the area of the triangle formed by ...

Find the area of the triangle formed by the tangents from the point (4, 3) to the circle `x^2+y^2=9` and the line joining their points of contact.

Text Solution

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In the figure, `OP =5` .
`:. PQ=4`.
In triangel OQP, `tan theta =(3)/(4)`
`:. `Area of triangle `PQR=(1)/(2)PQxxPR sin 2 theta`
`=(1)/(2) xx 4 xx 4xx(2 tan theta)/(1+tan^(2) theta )`
`=8(2((3)/(2)))/(1+((3)/(4))^(2))=(192)/(25)` sq. unit
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