Equal chords subtend equal angles at the center of a circle

Equal chords subtend equal angles at the center of a circle	If Angles subtended by the chords at the center of circle are equal, then chords are also equal	Perpendicular from the center of a circle to a chord bisects the chord	Line drawn from the center of circle to bisect a chord, is perpendicular to the chord	Equal chords are equidistant from the center of circle
Chords equidistant from the center of circle are equal in length

Before you understand the property, equal chords subtend equal angles at the center of a circle, you are advised to read: What are Chords of Circle ? What is center of Circle ? Observe the following diagram: In the above diagram, we have: A circle with center O PQ and RS are the chords of Circle Angle subtended by chord PQ at the center of circle is ∠ POQ Angle subtended by chord RS at the center of circle is ∠ ROS Now, you can observe also that: Chords PQ and RS are equal in length (as denoted by a green mark) So, per the property of circle "Equal chords subtend equal angles at the center of circle" , we get ∠ POQ = ∠ ROS Now, let's prove this property of equal chords subtend equal angles at the center of a circle in the following way: Before you prove this property of circle, you are advised to read: What are Congruent Triangles ? What is the SSS rule of Congruency ? What are the Corresponding Parts of Congruent Triangles ? What is the Radii of Circle ? Observe the following: In the above diagram, we have: A circle with center O PQ and RS are the chords of Circle Angle subtended by chord PQ at the center of circle is ∠ POQ Angle subtended by chord RS at the center of circle is ∠ ROS And we need to prove that: ∠ POQ = ∠ ROS In the above diagram, we have two Triangles (as highlighted below): △ PQO = △ RQO OP = OR (radii of circle are always equal) OQ = OS (radii of circle are always equal) PQ = RS (equal chords of circle - Given) Therefore, on applying SSS Rules of congruency, we get: ∆ PQO ≅ ∆ RQO Since, we know that corresponding parts of congruent triangles are equal, so we get: ∠ POQ = ∠ ROS Hence, this proves property "Equal chords subtend equal angles at the center of circle".