Question

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 C1 and C2externally. If a common tangent to C1 and C passing through P is also a common tangent to 2 and C1, then the radius of the circle C is 

Solution

Correct option is

8

Let A1A2 and M be the centres of the circles C1C2 and C respectively. Let the common tangent through P to C1 and C touch C1 at B1C at B2and C2 also at B2

From right angled triangle A1B1P

    

    

From triangle MPB2  

                

SIMILAR QUESTIONS

Q1

A circle with centre at the origin and radius equal to a meets the axis of x at A and B.P (α) and Q (β) are two points on this circle so that α – β = 2γ, where γ is a constant. The locus of the point of intersection of APand BQ is

Q2

A circle C1 of radius b touches the circle x2 + y2 = a2 externally and has its centre on the positive x-axis; another circle C2 of radius c touches the circle C1 externally and has its centre on the positive x-axis. Given ab < c, then the three circles have a common tangent if abc are in 

Q3

Angle of intersection of these circle is

Q4

If C1C2 are the centre of these circles than area of Δ OC1 C2, where Ois the origin, is

Q5

A triangle has two of its sides along the axes, its third side touches the circle x2 + y2 – 2ax – 2ay + a2 = 0. If he locus of the circumcentre of the triangle passes through the point (38, –37) then a2 – 2a is equal to

Q6

Two circles are inscribed and circumscribes about a square ABCD, length of each side of the square is 32. P and Q are points respectively of these circles, then  is equal to

Q7

Let A be the centre of the circle x2 + y2 – 2x – 4y – 20 = 0. The tangents at the point B(1, 7) and C(4, –2) on the circle meet at the point D. If Δ denotes the area of the quadrilateral ABCD, then 45Δ is equal to

Q8

If four distinct points (2, 3), (0, 2), (4, 5) and (0, t) are concylic, then t3+ 17 is equal to 

Q9

Equation of a tangent to the circle with centre (2, –1) is 3x + y = 0. The squar  of the length of the tangent to the circle from the point (23, 17) is

Q10

An equation of the circle through (1, 1) and the points of intersection ofx2 + y2 + 13x – 3y = 0 and 2x2 + 2y2 + 4x – 7y – 25 = 0 is