Q. 74.8( 12 Votes )

Prove that the li

Answer :

Given: CD and EF are two parallel tangents at points A and B of a circle with centre O.

To prove: AB passes through centre O or AOB is a diameter of the circle.

Construction: Join OA and OB. Draw OM || CD


Since, OM || CD,

OM || AC

We know that sum of adjacent interior angles is 180°.

CAO + MOA = 1 + 2 = 180°

We know that a tangent to a circle is perpendicular to the radius through the point of contact.

CAO = 90°

90° + MOA = 180°

MOA = 90°

Similarly, 3 = MOB = 90°

MOA + MOB = 90° + 90° = 180°

Thus, AOB is a straight line passing through O.

Ans. Hence, the line segment joining the points of contact of two parallel tangents of a circle passes through its centre.

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