Two Circles Touch Externally at a point C. AB is a common tangent to both of these circles. Find the angle ACB.

Asked by Vaibhav Tomar | 3rd Feb, 2014, 12:39: AM

Expert Answer:

 
Let C1 and C2 be the two circles with centres P and Q respectively.
 
AB is a common tangent to both the circles at C.
 
Since AB is a tangent to C1, angle P C A equals 90 degree
Similarly, AB is a tangent to C2, angle Q C A equals 90 degree
Thus adding the above two angles, we have
 
angle P C A plus angle Q C A equals 180 degree
rightwards double arrow angle P C Q equals 180 degree rightwards double arrow P C Q space i s space a space s t r a i g h t space l i n e
 
Since AB is perpendicular to the line joining the centres,
 
angle A C P plus angle P C B equals 180 degree rightwards double arrow A C B equals 180 degree

Answered by  | 3rd Apr, 2014, 12:55: PM

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