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प्रश्न
If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.
उत्तर
Let AB and AC be two chords and AOD be a diameter such that
∠ BAO = ∠ CAO
Draw OL ⊥ AB and OM ⊥ AC.
Now prove, Δ OLA = Δ OMA
Then OL = OM ⇒ AB = CD. .....(Chords which are equidistant from the centre are equal.)
Hence proved.
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संबंधित प्रश्न
AB and CD are two equal chords of a circle with centre O which intersect each other at right
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Given O is the centre of the circle and ∠AOB = 70°. Calculate the value of:
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- ∠ABC,
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- ∠DCA,
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- ∠DCI,
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Prove that the chords are parallel.
The length of the common chord of two intersecting circles is 30 cm. If the diameters of these two circles are 50 cm and 34 cm, calculate the distance between their centers.
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Calculate:
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