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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
Suppose CD and AB are two parallel tangents of a circle with center O
Construction: Draw a line parallel to CD passing through O i.e. OP
We know that the radius and tangent are perpendicular at their point of contact.
∠OQC = ∠ORA = 90°
Now, ∠OQC + ∠POQ = 180° (co-interior angles)
⇒ ∠POQ = 180° - 90° = 90°
Similarly, Now, ∠ORA +∠POR =180° (co-interior angles)
⇒ ∠POQ = 180° - 90° = 90°
Now,∠POR + ∠POQ = 90° + 90° =180°
Since, ∠POR and ∠POQare linear pair angles whose sum is 180°
Hence, QR is a straight line passing through center O.
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