Edu Simulation

📐 Experiment 1: The line joining the center of a circle and the mid-point of a chord is perpendicular to the chord.

Figure I

Figure II

Figure	∠OCA	∠OCB	Result
(I)	—	—	—
(II)	—	—	—

Statement: The line drawn through the center of a circle to bisect a chord is perpendicular to the chord.

In a given figure, O is a center of a circle and CD is a chord in which CM = MD.

OM ⊥ CD

S. No.	Statements	S. No.	Reasons
1.	In ΔOMC and ΔOMD	1.
(i)	OC = OD (s)	(i)	Radius of the same circle
(ii)	OM = OM (s)	(ii)	Common side
(iii)	CM = DM (s)	(iii)	Given CM = DM
2.	ΔOMC ≅ ΔOMD	2.	By SSS theorem
3.	∠OMC = ∠OMD	3.	Corresponding angles of congruent triangle
4.	∠OMC + ∠OMD = 180° ∠OMC + ∠OMC = 180° or, 2∠OMC = 180° or, ∠OMC = 90°	4.	The sum of adjacent angles in a straight line
5.	OM ⊥ CD	5.	From statement 4 ∠OMC = 90°

Proved.

Identification and Verification of the Properties of Circle