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दी गई आकृति में, O वृत्त का केंद्र है। MN एक जीवा है तथा बिंदु M पर स्पर्श-रेखा ML इस प्रकार है कि यह MN के साथ 70° का कोण बनाती है। ∠MON का माप है :

O is the centre of the circle. MN is the chord and the tangent ML at point M makes an angle of 70° with MN.

(A) 120°

(B) 140°

(C) 70°

(D) 90°

1 Answer

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सही विकल्प है (B) 140°

हम जानते हैं कि त्रिज्या स्पर्शरेखा पर लंबवत होती है।

\(\therefore \angle OML = 90^\circ\)

\(\Rightarrow \angle O M N+\angle N M L =90^{\circ}\)

\(\Rightarrow \angle O M N+70^{\circ} =90^{\circ}\)

\(\Rightarrow \angle O N N =90^{\circ}-70^{\circ}\)

\(\Rightarrow \angle O M N =20^{\circ}\)

\(O M=O N\quad[\text {Radii of a Circle] }\)

\(\angle OMN=\angle O N M=20^{\circ} \quad \text{[Base angles of equal sides are also equal]}\)

\(\triangle MON\) में,

\(\angle O M N+\angle M O N+\angle O N M=180^{\circ} \quad \mathrm{[\because Sum\ of \ angles\ of\ a\ triangle\ is\ 180^\circ]}\)

\(20^{\circ}+\angle M O N+20^{\circ} =180^{\circ}\)

\(\angle M O N+40^{\circ} =180^{\circ} \)

\(\angle M O N =180^{\circ}-40^{\circ} \)

\(\therefore \angle M O N =140^{\circ}\)

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