Show that if two circles have the same radius, then their equal chords form equal angles at the centres.
Given: Two Congruent Circles \(C_1\) and \(C_2\)
\(CD\) is the chord of \(C_1\) and
\(YZ\) is the chord of \(C_2\)
Also, \(CD =YZ \)
To Prove: Angle subtended by the Chords CD and YZ are equal
That is, \(∠COD = ∠YXZ\)
Proof:
In \(△COD\) and \(△YXZ\)
\(CO =\) ()
\(DO =\) ()
\( CD=\) (Given)
\(△COD ⩭ △YXZ\) ()
Therefore, \(∠COD = ∠YXZ\) ()
Answer variants:
\(YX\)
CZ
\(YZ\)
\(ZX\)