Question

In a circle, if two chords are equal, prove they subtend equal angles at the center. (NCERT Class 9/10)

Answer: Equal chords AB and CD in circle with center O imply OA=OB=OC=OD (radii). Triangles OAB and OCD have three equal sides ⇒ congruent (SSS), so central angles ∠AOB=∠COD.

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Question

In a circle, if two chords are equal, prove they subtend equal angles at the center. (NCERT Class 9/10)

Answer: Equal chords AB and CD in circle with center O imply OA=OB=OC=OD (radii). Triangles OAB and OCD have three equal sides ⇒ congruent (SSS), so central angles ∠AOB=∠COD.