Three circles lie on a plane such that each o | vedclass

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

Question

(D) Let the centers of the circles be $C_1, C_2, C_3$ with radii $r_1=3, r_2=3, r_3=1$. The sides of the triangle $C_1C_2C_3$ are $C_1C_2 = 3+3=6$,$C_

Vedclass · Accepted Answer

None of these

Vedclass · Answer

(D) Let the centers of the circles be $C_1, C_2, C_3$ with radii $r_1=3, r_2=3, r_3=1$. The sides of the triangle $C_1C_2C_3$ are $C_1C_2 = 3+3=6$,$C_1C_3 = 3+1=4$,and $C_2C_3 = 3+1=4$.This is an isosceles triangle. Let $M$ be the midpoint of $C_1C_2$. The height $h = C_3M = \sqrt{4^2 - 3^2} = \sqrt{7}$.Points $A$ and $B$ lie on $C_1C_3$ and $C_2C_3$ respectively. By similar triangles,the side length $AB$ of triangle $ABC$ is $\frac{AB}{C_1C_2} = \frac{C_3A}{C_3C_1} = \frac{4-3}{4} = \frac{1}{4}$. Thus,$AB = \frac{1}{4} 	imes 6 = \frac{3}{2}$.The height of triangle $ABC$ from $C$ to $AB$ is $h' = h - (	ext{distance of } C 	ext{ from } AB) = \sqrt{7} - \frac{3}{4}\sqrt{7} = \frac{\sqrt{7}}{4}$.Area of $	riangle ABC = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height} = \frac{1}{2} 	imes \frac{3}{2} 	imes \frac{\sqrt{7}}{4} = \frac{3\sqrt{7}}{16}$.

Three circles lie on a plane such that each of them externally touches the other two. Two of them have radius $3$,and the third has radius $1$. If $A, B$,and $C$ are the points of tangency of the circles,then the area of the triangle $ABC$ is

Similar Questions

Two circles each of radius $5$ units touch each other at $(1,2)$ and $4x+3y=10$ is their common tangent. The equation of that circle among the two given circles,such that some portion of it lies in every quadrant is

Let the point $P$ be the vertex of the parabola $y = x^2 - 6x + 12$. If a line passing through the point $P$ intersects the circle $x^2 + y^2 - 2x - 4y + 3 = 0$ at the points $R$ and $S$, then the maximum value of $(PR + PS)^2$ is:

$A$ focal chord to $y^2 = 16x$ is a tangent to $(x - 6)^2 + y^2 = 2$. Then the possible values of the slope of this chord are:

Let $a$ and $b$ be non-zero real numbers. Then,the equation $(a x^2+b y^2+c)(x^2-5 x y+6 y^2)=0$ represents

If the lines $kx + 2y - 4 = 0$ and $5x - 2y - 4 = 0$ are conjugate with respect to the circle $x^2 + y^2 - 2x - 2y + 1 = 0$,then $k$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module