Circle theorems:-
Today in this article I will discuss on circle theorems which are for school going students of class 9 and class 10
- Prove that perpendicular drawn from the center of a circle intersect a chord bisects the chord.
Answer:-
In the picture, a circle is drawn with center 'O' AB is a chord of the circle. Perpendicular drawn from the center 'O' on the chord AB. i.e; OC⊥ AB
To prove that:- OC bisects AB,i.e; AC = BC
Construction:- OA and OB are drawn.
Proof:- In between Δs AOC and BOC we get,
∵ OA = OB [ ∵ radii of the same circle]
∵ OC = OC [ ∵ Common side of the Δs]
∵ ∠OCA = ∠OCB [ ∵ both are 90°]
∴ Δ AOC ≌ Δ BOC [ By SAS congruence rule of the Δs]
∴ AC = BC [∵ By CPCT] Proved
- Prove that line joining the midpoint of a chord of a circle bisects the chord is perpendicular on the chord.
