Question

In the figure AC is a common tangent of two touching circles. If B is touching point of both circles then find angle B.

Answer 1

Answer : angle ABC===90 degrees

Let small circle center C1 and radius be x and larger cirlce center C2 and radius y.

we know C1A is perpendicular to AC and similarly for C2C this means they are parallel , now join C1D parallel to AC cutting C2C at point D .Hence C1DCA is a rectangle Now join C1 B C2 line .

Let (angle) <BC1D=a ==== <DC2C1==90-a

Now in triangle C1AB , C1A=C1B = x ;;;;<C1BA=(90-a)/2

and similarly in triangle CC2B ,BC2=CC2=y;;;; <CBC2 ==(90+a)/2

now by linear pair <ABC will be == 180 - [(90-a)/2 + (90+a)/2] ==== 90