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प्रश्न
Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.
उत्तर
et XBY and PCQ be two parallel tangents to a circle with centre O.
Construction: Join OB and OC.
Draw OA∥XY
Now, XB∥AO
⇒ ∠XBO + ∠AOB = 180° (sum of adjacent interior angles is 180°)
Now, ∠XBO = 90° (A tangent to a circle is perpendicular to the radius through the point of contact)
⇒ 90° + ∠AOB = 180°
⇒ ∠AOB = 180° − 90° = 90°
Similarly, ∠AOC = 90°
∴ ∠AOB + ∠AOC = 90° + 90° = 180°
Hence, BOC is a straight line passing through O.
Thus, the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.
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