Angles subtended by chords of a circle for Competitive Exam – Quantitative Aptitude

Angles subtended by chords of a circle(वृत्त की जीवाओं द्वारा अंतरित कोण) In Hindi

Angles subtended by chords of a circle(वृत्त की जीवाओं द्वारा अंतरित कोण) :- एक वृत्त की समान जीवाएँ केंद्र पर समान कोण बनाती हैं।

प्रमेय –  यदि किसी वृत्त की जीवाओं द्वारा केंद्र पर अंतरित कोण बराबर हों, तो जीवाएँ बराबर होती हैं।

Angles subtended by chords of a circle In English

Angles subtended by chords of a circle :- If the angles subtended by the chords of a circle at the center are equal, then the chords are equal.

Theorem:-  Equal Chords, Equal Angles: If you have two chords in a circle that are the same length, then the angles they subtend at the center of the circle will also be equal.

To prove: ∠ AOC = ∠ BOD.
In triangles, AOC and BOD,
OA = OB (Radius of a circle)
OC = OD (Radius of a circle)
AB = CD (Equal chords)
By, using Side-Side-Side (SSS Rule), we can write:
∆ AOB ≅ ∆ COD
As the triangles are congruent, the angles should be of equal measurement.
Therefore, ∠ AOB = ∠ COD Proved