The centres of two circles C1 and `C2` each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1` and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is

The centres of two circles C1 and `C2` each of unit radius are at a di

1.	The centres of two circles C1 and `C2` each of unit radius are at a distance of 6 units from each other. Let P be the mid point of the line segment joining the centres of C1` and C2 and C be a circle touching circles C1 and C2 externally. If a common tangent to C1 and C passing through P is also a common tangent to C2 and C, then the radius of the circle C is
Answer» in `/_ PDO` `/_PRO = 90^@`angle between tangent let `/_ POR = alpha` `/_APD = alpha = /_EPB` (V.O.A) In `/_ PEB` `BE=1` (radius) `BP= 3` `PE^2 = BD^2 - BE^2` `PE^2 = 9 - 1` `PE = 2 sqrt(2)` `tan alpha = (BE)/(PE) = 1/(2sqrt(2))` in ` /_PDO ` `tan alpha = (PD)/(DO) = (PD)/R` `R= (PD)/tan alpha = (2 sqrt(2))/(1/(2sqrt2))` `R=8`units

Discussion

No Comment Found

Related InterviewSolutions

Find the ratio in which the x-axis cuts the join of the points A(4,5) and B(-10,-2). Also, find the point of intersection.
If the origin is shifted to the point (-3,-2) by a translation of the axes, find the new coordinates of the point (3,-5).
The distance between the lines `5x-12y+65=0` and `5x-12y-39 = 0` is :A. 4B. 16C. 2D. 8
Prove that the locus of the centroid of the triangle whose vertices are`(acost ,asint),(bsint ,-bcost),`and `(1,0)`, where `t`is a parameter, is circle.A. `(3x -1)^(2) + (3y)^(2) = a^(2) - b^(2)`B. `(3x -1)^(2) + (3y)^(2) = a^(2) + b^(2)`C. `(3x + 1)^(2) + (3y)^(2) = a^(2) + b^(2)`D. ` (3x + 1)^(2) + (3y)^(2) = a^(2) - b^(2)`
Prove that the locus of the centroid of the triangle whose vertices are`(acost ,asint),(bsint ,-bcost),`and `(1,0)`, where `t`is a parameter, is circle.A. `(3x+1)^(2) + (3y)^(2) = a^(2) - b^(2)`B. `(3x - 1)^(2) = a^(2) - b^(2)`C. `(3x -1)^(2) + (3y)^(2) = a^(2) + b^(2)`D. `(3x + 1)^(2) + (3y)^(2) = a^(2) + b^(2)`
For `a gt b gt c gt 0`, if the distance between `(1,1)` and the point of intersection of the line `ax+by-c=0` and `bx+ay+c=0` is less than `2sqrt2` then,(A) `a+b-cgt0` (B) `a-b+clt0` (C) `a-b+cgt0` (D) `a+b-clt0`A. `a+b-c gt 0`B. `a-b+c lt 0`C. `a-b+c gt0`D. `a+b-c lt 0`
ABC is a triangle formed by the lines xy = 0 and x + y = 1 . Statement - 1 : Orthocentre of the triangle ABC is at the origin . Statement - 2 : Circumcentre of `Delta`ABC is at the point (1/2 , 1/2) .A. Statement -1 is True , Statement - 2 is true , Statement- 2 is a correct explanation for statement - 12B. Statement-1 is True , Statement-2 is True , Statement -2 is not a correct explanation for Statement - 1 .C. Statement-1 is True , Statement - 2 is False .D. Statement - 1 is False , Statement -2 is True .
Find the equations of the altitudes of a `triangle ABC`, whose vertices are A(2,-2), B(1,1) and C(-1,0).
The orthocentre of the triangle formed by the lines `x=2,y=3` and `3x+2y=6` is at the pointA. (2,0)B. (0,3)C. (2,3)D. none of these
If A(0, 0), B(2, 4) and C(6, 4) are the vertices of a `triangle ABC`, find the equations of its sides.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment