If two chords of a circle are equally inclined to the diameter through

1.	If two chords of a circle are equally inclined to the diameter throughtheir point of intersection, prove that the chords are equal
Answer» given: AB is the diameter of the circle with center O. ∠BAC=∠BAD TPT: AC=AD construction; draw OM⊥AC and ON⊥AD proof: in the triangle OMA and triangle ONA, ∠OMA=∠ONA=90 deg (by the construction) ∠OAM=∠OAN OA is common. therefore by AAS congruency, triangles are congruent. hence by the congruent property of the triangles OM = ON ⇒AC = AD [equal chords are equidistant from center ] which is the required result.

If two chords of a circle are equally inclined to the diameter throughtheir point of intersection, prove that the chords are equal

Answer»

given: AB is the diameter of the circle with center O.

∠BAC=∠BAD

TPT: AC=AD

construction; draw OM⊥AC and ON⊥AD

proof:

in the triangle OMA and triangle ONA,

∠OMA=∠ONA=90 deg (by the construction)

∠OAM=∠OAN

OA is common.

therefore by AAS congruency, triangles are congruent.

hence by the congruent property of the triangles OM = ON

⇒AC = AD [equal chords are equidistant from center ]

which is the required result.