Line drawn from the center of circle to bisect a chord, is perpendicular to the chord

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, line drawn from the center of circle to bisect a chord is perpendicular to the chord, you are advised to read: What are Chords of Circle ? What is center of Circle ? What is Perpendicular ? Observe the following diagram: In the above diagram, we have: A circle with center O XY is the chord of Circle M is the point of intersection of Line AB and Chord XY, such that: XM = MY (as highlighted by green) Now, you can also observe that: Line AB passes through the center O and M is the mid-point of Chord XY. So, as per the property of circle "The line drawn from the center of circle to bisect a chord is perpendicular to the chord", so we get: Line AB is perpendicular to Chord XY Or we can write it as: Angle OMX = Angle OMY = 90 degree each Now, let's prove this property, line drawn from the center of circle to bisect a chord is perpendicular to the chord in the following way: Before you prove this property of circle, you are advised to read: What are Congruent Triangles ? What is 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 XY is the chord of Circle Line AB passes through the center O M is the mid-point of Chord XY and we get: XM = MY (as highlighted by green) And we need to prove that: ∠ OMX = ∠ OMY = 90° each Now, join point O & X and O & Y (as shown below) This would give us two triangles i.e. (as highlighted below): △ XOM = △ YOM OX = OY (radii of circle are always equal) OM = OM (common side) XM = MY (given) Therefore, on applying SSS Rules of congruency, we get: ∆ XOM ≅ ∆ YOM Since, we know that corresponding parts of congruent triangles are equal, so we get: ∠ OMX = ∠ OMY ... (statement 1) Now, you can see that ∠ OMX and ∠ OMY form a linear pair, so we get: ∠ OMX + ∠ OMY = 180° As proved above in statement 1, ∠ OMX = ∠ OMY, so we get: ∠ OMX + ∠ OMX = 180° 2 ∠ OMX = 180° Divide both sides by 2 and we get: ∠ OMX = 90° Therefore this proves: ∠ OMX = ∠ OMY = 90° each. Hence, this proves property "The line drawn from the center of circle to bisect a chord is perpendicular to the chord"