Two tangents drawn from P(1, 7) to the circle | vedclass

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(C) The circle is $x^2 + y^2 = 25$,so its center $O$ is $(0, 0)$ and radius $r = 5$.Length of the tangent segment from $P(1, 7)$ to the circle is give

Vedclass · Accepted Answer

$25 	ext{ sq. units}$

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(C) The circle is $x^2 + y^2 = 25$,so its center $O$ is $(0, 0)$ and radius $r = 5$.Length of the tangent segment from $P(1, 7)$ to the circle is given by $\sqrt{x_1^2 + y_1^2 - r^2} = \sqrt{1^2 + 7^2 - 25} = \sqrt{1 + 49 - 25} = \sqrt{25} = 5$.In the quadrilateral $PQOR$,$PQ$ and $PR$ are tangents,so $PQ = PR = 5$.Also,$OQ = OR = 5$ (radii of the circle).Since the tangent is perpendicular to the radius at the point of contact,$\angle OQP = \angle ORP = 90^{\circ}$.The quadrilateral $PQOR$ consists of two congruent right-angled triangles,$	riangle PQO$ and $	riangle PRO$.Area of $	riangle PQO = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes PQ 	imes OQ = \frac{1}{2} 	imes 5 	imes 5 = 12.5 	ext{ sq. units}$.Total area of quadrilateral $PQOR = 2 	imes 	ext{Area of } 	riangle PQO = 2 	imes 12.5 = 25 	ext{ sq. units}$.

Two tangents drawn from $P(1, 7)$ to the circle $x^2 + y^2 = 25$ touch the circle at $Q$ and $R$ respectively. The area of the quadrilateral $PQOR$ is

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