Question

Two circles touch externally and through the point of contact a straight line is drawn to cut both
the circles. Show that the tangents at the extremities of this line are parallel to each other.
is the diameter of the​

Answer 1

Answer:

Join OO', OB and O'C

In triangle OAB, we have:

OA = OB

angle OBA = angle OAB (1)

In triangle O'AC, we have:

O'A = O'C

angle O'CA = angle O'AC (2)

But, angle OAB = angle O'AC

Using (1) and (2),

angle OBA = angle O'CA

Thus, tangents at B and C are two lines and BC is a transversal such that alternate angles are equal.

Hence, the tangents at B and C are parallel.

Answered