Question

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In two concentric circles, prove that the all chords of the outer circle, which touch the inner circle are of equal length.​

Answer 1

for solution refer attachment

Answer 2

Step-by-step explanation:

Let the two concentric circles be C₁ and C₂ With Center O. Two Chords of outer circle C₁ touch inner circle C₂ at M and N.

Proof: PQ = RS.

From figure:

OM and ON are radii of the inner circle through the points of contact M and N of the tangents PQ and RS.

∴ OM ⊥ PQ and ON ⊥ RS. Also, OM = ON.

∴ PQ and RS are two chords of the outer circle C₁ which are equidistant from its centre O.

Therefore, PQ = RS.

Hence, all such chords are equal in length.

Hope it helps!