Three circles of radii 1, 2 and 3 units respe | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let the centers of the circles be $A, B$ and $C$ with radii $r_1 = 3, r_2 = 2$ and $r_3 = 1$ respectively.Since the circles touch each other exter

Vedclass · Accepted Answer

$2.5$

Vedclass · Answer

(C) Let the centers of the circles be $A, B$ and $C$ with radii $r_1 = 3, r_2 = 2$ and $r_3 = 1$ respectively.Since the circles touch each other externally,the distances between the centers are the sum of their radii:$AB = r_1 + r_2 = 3 + 2 = 5$$BC = r_2 + r_3 = 2 + 1 = 3$$AC = r_1 + r_3 = 3 + 1 = 4$In $	riangle ABC$,we observe that $AB^2 = 5^2 = 25$ and $BC^2 + AC^2 = 3^2 + 4^2 = 9 + 16 = 25$.Since $AB^2 = BC^2 + AC^2$,$	riangle ABC$ is a right-angled triangle with the hypotenuse $AB = 5$.The circumradius $R$ of a right-angled triangle is half of its hypotenuse.$R = \frac{AB}{2} = \frac{5}{2} = 2.5$ units.

Three circles of radii $1, 2$ and $3$ units respectively touch each other externally in the plane. The circumradius of the triangle formed by joining the centers of the circles is

Similar Questions

The triangle $PQR$ is inscribed in the circle $x^2+y^2=25$. If $Q=(3,4)$ and $R=(-4,3)$,then $\angle QPR=$

For the circle $x^2 + y^2 - 2x + 4y - 4 = 0$,what is the line $2x - y - 1 = 0$?

If the straight line $y=mx$ lies outside of the circle $x^2+y^2-20y+90=0$, then the value of $m$ will satisfy

The equation of a circle passing through the point $(2,8)$,touching the lines $4x-3y-24=0$ and $4x+3y-42=0$,and having the $x$-coordinate of its centre less than or equal to $8$ is

For what values of $m$ does the circle $x^2 + y^2 = 4x + 8y + 5$ intersect the line $3x - 4y = m$ at two distinct points?

Vedclass Test Series

Exam Paper Generator

Online Exam Module