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Prove that the chords inclined on the sa...

Prove that the chords inclined on the same angle to the radius or diameter of a circle are equal in length.

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Given: AB and AC are two chords of a circle with centre `O`, AN is the diameter of the circle and `angle BAN=angle CAN`
To Prove: `AB=AC`
Construction : Draw `OPbotAB` and `OQbotAC`.
Proof: In `Delta OPA` and ` Delta OQA`,
`because" "{(angleOPA,=,,angle OQA,("each "90^@)),(angleOAP,=,,angleOAQ,("given")),(OA,=,,OA,("common")):}`
`therefore Delta OPAcongDeltaOQA`(A.A.S.congruency)
`rArrOP=OQ` (c.p.c.t)
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