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  • The line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle. (True/False)Option: 1 True

The line segment joining the points of contact of two parallel tangents to a circle is a diameter of the circle. (True/False)

Option: 1

True


Option: 2

False


Answers (1)

best_answer

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

Join OA and OB. Draw OG || CD

\begin{array}{l} \therefore \quad \angle C A O+\angle G O A=180^{\circ} \\ \Rightarrow \quad \angle 90^{\circ}+\angle G O A=180^{\circ} \quad[\because O A \perp C D] \\ \Rightarrow \quad \angle G O A=90^{\circ} \end{array}

\begin{array}{l} \text { Similarly, } \angle G O B=90^{\circ} \text { . } \\ \therefore \quad \angle G O A+\angle G O B=90^{\circ}+90^{\circ}=180^{\circ} \end{array}

AOB is a straight line. Hence, AOB is a diameter of the circle with centre O.

So, the statement is true

Posted by

sudhir.kumar

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