In the figure given, two circles with centres `C_1 and C_2`, are 35 units apart,i.e. `C_1C_2 = 35`. The radii of the circles with centres `C_1 and C_2`, are 12 and 9 respectively. If P is the intersection of `C_1C_2`, and a common internal tangent to the circles, then `l(C_1P)` equals

In the figure given, two circles with centres C_t and C_2 are 35 units apart, i.e. C_1 C_2=35 . The radii of the circles with centres C_1 and C_2 are 12 and 9 respectively. If P is the intersection of C_1 C_2 and a common internal tangent to the circles, then l(C_1 P) equals

In the figure given,two circles with centres C_(1) and C_(2), are 35 units apart,i.e.C_(1)C_(2)=35 .The radii of the circles with centres C_(1) and C_(2), are 12 and 9 respectively.If P is the intersection of C_(1)C_(2, and a common ) internal tangent to the circles,then l(C_(1)P) equals

The radical axis of two circles having centres at C_(1) and C_(2) and radii r_(1) and r_(2) is neither intersecting nor touching any of the circles, if

The radical axis of two circles having centres at C_(1) and C_(2) and radii r_(1) and r_(2) is neither intersecting nor touching any of the circles, if

Three circles with centres C_(1),C_(2) and C_(3) and radii r_(1),r_(2) and r_(3) where *r_(-)1

Circles C_1 and C_2 are externally tangent and they are both internally tangent to the circle C_3. The radii of C_1 and C_2 are 4 and 10, respectively and the centres of the three circles are collinear. A chord of C_3 is also a common internal tangent of C_1 and C_2. Given that the length of the chord is (msqrtn)/p where m,n and p are positive integers, m and p are relatively prime and n is not divisible by the square of any prime, find the value of (m + n + p).

The internal common tangents to two circles with centre C_1 and C_2 intersect the line joining C_1 and C_2 at P and the two direct common tangents intersects the line joining C_1 and C_2 at Q. The length C_1P , C_1C_2 and C_1 Q are in

C_(1) and C_(2) are two concentric circles with centres at O. Their radii are 12 cm and 3 cm respectively. B is the point of contact of tangents drawn to C_(2) from a point A lying on the circle C_(1) . Then the area of the triangle OAB is :

The lengths of the tangents from A(-3,5) and B(1,2) to a circle are 6 and 5 respectively.Then the length of the tangent from C(5,-1) to the same circle is