Equal Chords are Equidistant from the Center of Circle
Equal Chords are Equidistant from the Center of Circle
Theorem 1 Equal chords of a circle are equidistant from the centre
Given Two chords AB and CD of a circle C (O,r) such that AB = CD and OL To prove Chords AB and CD are equidistant from the centre O i.e, OL = OM. CONSTRUCTION Join OA and OC. PROOF Since the perpendicular from the centre to a chord bisects the chord Therefore, and, But,
Now, in right triangles OAL and OCM, we have and, So, by RHS criterion of convergence, we have Hence, equal chords of a circle are equidistant from the centre. |  |
Theorem 2 Chords of a circle which are equidistant from the centre are equal.
Given Two chords AB and CD of a circle C(O,r) which are equidistant from its centre i.e., OL = OM, where OL AB and OM
CD.
TO PROVE Chords are equal i.e AB = CD CONSTRUCTION Join OA and OC PROOF Since the perpendicular from the centre of a circle to a chord bisects the chord. Therefore,
and,
In, triangles OAL and OCM , we have
and, So, by RHS< criterion of convergence, we have
Hence, the chords of a circle which are equidistant from the centre are equal. | |
Illustration:
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| Right Option : B | |||||
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| Right Option : B | |||||
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| Right Option : D | |||||
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9thAbhyas institute is one of the best coaching institute in the vicinity of Ambala Cantt area. The teachers of the institute are well experienced and very helpful in solving the problems of the students.The good thing of the institute is that it is providing extra classes for the students who are w...
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