The radius of the circumcircle of the triangle PRS is, Consider the circle and the parabola . They intersect at P and Q in the first and the fourth quadrants, respectively. [2007]

Question

Consider the circle $x^{2} + y^{2} = 9$ and the parabola $y^{2} = 8 x$ . They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the circle at P and Q intersect the $x$ -axis at R and tangents to the parabola at P and Q intersect the $x$ -axis at S. [2007]

Q. The radius of the circumcircle of the triangle $P R S$ is

Smart Achievers · Accepted Answer

(2)

$For ∆ P R S,$

$area (∆ P R S) = Δ = \frac{1}{2} \times S R \times P T = \frac{1}{2} \times 10 \times 2 \sqrt{2} = 10 \sqrt{2},$

$a = P S = 2 \sqrt{3}, b = P R = 6 \sqrt{2}, c = S R = 10$

$∴$ $Radius of circumcircle of ∆ P R S,$

$R = \frac{a b c}{4 Δ} = \frac{2 \sqrt{3} \times 6 \sqrt{2} \times 10}{4 \times 10 \sqrt{2}} = 3 \sqrt{3}$

Solution

1 $5$

2 $3 \sqrt{3}$

3 $3 \sqrt{2}$

4 $2 \sqrt{3}$

Want Us to Email you About Special Offers & Updates?

Solution

1 5

2 33

3 32

4 23

Ans. (2) For ∆PRS, area(∆PRS)=Δ=12×SR×PT =12×10×22=102, a=PS=23, b=PR=62, c=SR=10 ∴ Radius of circumcircle of ∆PRS, R=abc4Δ=23×62×104×102=33

Want Us to Email you About Special Offers & Updates?

1 $5$

2 $3 \sqrt{3}$

3 $3 \sqrt{2}$

4 $2 \sqrt{3}$