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


Proof:


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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