Question

Prove that the line segment joining the points of contact of 2 parallel tangents of a circle, passes through the center of the circle

Answer 1

Hey mate!!

Let the center of the circle be O.  Let there be two tangents T1 and T2 touching the circle at P and Q. Let T1 and T2 be parallel.

Join PO and OQ.  We know PO ⊥ T1   and  OQ ⊥ T2 (radius & tangent).

Hence,  OQ ⊥ T1  (as T1 || T2).

Hence,   PO || OQ .   Both have common point O.  Hence  POQ is a single straight line.

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