From the point P(16, 7) tangents PQ and PR are drawn to the circle x2+y2-2x-4y-20=0 .If c be the centre of the circle, then area of quadrilateral PQCR is

Question

From the point P(16, 7) tangents PQ and PR are drawn to the circle x2+y2-2x-4y-20=0 .If c be the centre of the circle, then area of quadrilateral PQCR is (A)  450 sq unit  (B)  15 sq unit  (C)  50 sq unit  (D)  75 sq unit

Tardigrade Admin · Accepted Answer

If tangents are drawn from a point to the circle, then quadrilateral

PQCR

makes two equal right triangles. Given, equation of circle is

x^{2} + y^{2} - 2 x - 4 y - 20 = 0

∴

Centre is

(1, 2)

and radius,

r = 1^{2} + 2^{2} + 20

= 25 = 5

Now,

PC = (16 - 1)^{2} + (7 - 2)^{2}

= 225 + 25

= 250

In

Δ PCQ

,

PQ = P C^{2} - Q C^{2}

= (250)^{2} - (5)^{2}

= 250 - 25

= 225

= 15

∴

Area of quadrilateral

PQCR

= 2

area of

Δ PCQ

= 2 \cdot \frac{1}{2} PQ \cdot QC

= 1 \cdot 15 \cdot 5

= 75 s q u ni t

Q. From the point $P (16, 7)$ tangents $PQ$ and $PR$ are drawn to the circle $x^{2} + y^{2} - 2 x - 4 y - 20 = 0$ .If $c$ be the centre of the circle, then area of quadrilateral $PQCR$ is

$450 s q u ni t$

$15 s q u ni t$

$50 s q u ni t$

$75 s q u ni t$

Q. From the point P(16,7) tangents PQ and PR are drawn to the circle x2+y2−2x−4y−20=0 .If c be the centre of the circle, then area of quadrilateral PQCR is

450squnit

15squnit

50squnit

75squnit

Q. From the point $P (16, 7)$ tangents $PQ$ and $PR$ are drawn to the circle $x^{2} + y^{2} - 2 x - 4 y - 20 = 0$ .If $c$ be the centre of the circle, then area of quadrilateral $PQCR$ is

$450 s q u ni t$

$15 s q u ni t$

$50 s q u ni t$

$75 s q u ni t$