AB is the common tangent to the circles `C_1` and `C_2`. `C_1` and `C_2` are touching externally at C.AD and DC are two chords of the circle `C_1` and BE and CE are two chords of the circle `C_2`. Find the measure of `/_ADC+/_BEC`

In the following figure, (not a scale), AB is the common tangent to the circles C_1 and C_2 and C_1 and C-2 are touching externally at C. AD and DC are two chords of the circle, C_1and BE and CE are two chords of the circle C_2 . Find the measure of angle ADC+ angle BEC .

Two circles touch externally at P. A direct common tangent AB to two circles touch the circles at A and B. Then the measure of angleAPB is

In the figure, chord AB || tangent DE. Tangent DE touches the circle at point C then prove AC = BC.

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

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).

In the given figure (not to scale), two circles C_1 and C_2 intersect at S and Q. PQN and RQM are tangents drawn to C_1 and C_2 respectively at Q. MAB and ABN are the chords of the circles C_1 and C_2 . If angle NQR =85^@ , then find angle AQB .

Consider circles C_(1) and C_(2) touching both the axes and passing through (4, 4), then the x - intercept of the common chord of the circles is

The centres of two circles C_1 and C_2, 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 C_1 and C_2, and C be a circle touching circles C_1 and C_2 externally. If a common tangent to C_1 and C passing through P is also a common tangent to C_2 and C. then the radius of the circle C is.