If and are the radii of smallest and largest circles which pass through (5, 6) and touch the circle, then is

Question

If $r_{1}$ and $r_{2}$ are the radii of smallest and largest circles which pass through (5, 6) and touch the circle ${(x - 2)}^{2} + y^{2} = 4$ , then $4 r_{1} r_{2}$ is

Smart Achievers · Accepted Answer

(2)

${(x - 2)}^{2} + y^{2} = 4$

$Centre is (2, 0) and radius = 2$

$Distance between (2, 0) and (5, 6) = \sqrt{9 + 36} = 3 \sqrt{5}$

$∴$ $r_{1} r_{2} = \frac{(3 \sqrt{5} - 2) (3 \sqrt{5} + 2)}{4} = \frac{41}{4}$

$∴$ $4 r_{1} r_{2} = 41$

Solution

Q.
If $r_{1}$ and $r_{2}$ are the radii of smallest and largest circles which pass through (5, 6) and touch the circle ${(x - 2)}^{2} + y^{2} = 4$ , then $4 r_{1} r_{2}$ is

1 $\frac{4}{41}$

2 $41$

3 $\frac{5}{41}$

4 $\frac{41}{6}$

Ans.
(2)

${(x - 2)}^{2} + y^{2} = 4$

$Centre is (2, 0) and radius = 2$

$Distance between (2, 0) and (5, 6) = \sqrt{9 + 36} = 3 \sqrt{5}$

$∴$ $r_{1} r_{2} = \frac{(3 \sqrt{5} - 2) (3 \sqrt{5} + 2)}{4} = \frac{41}{4}$

$∴$ $4 r_{1} r_{2} = 41$

Want Us to Email you About Special Offers & Updates?

Solution

Q. If r1 and r2 are the radii of smallest and largest circles which pass through (5, 6) and touch the circle (x-2)2+y2=4, then 4r1r2 is

1 441

2 41

3 541

4 416

Ans. (2) (x-2)2+y2=4 Centre is (2,0) and radius=2 Distance between (2,0) and (5,6)=9+36=35 ∴ r1r2=(35-2)(35+2)4=414 ∴ 4r1r2=41