Theorem on Circles CBSE Class IX ICSE Class X (Perpendicular Theorem)
In a circle a line drawn from centre of a circle ^ to a chord bisect the chord.
Circle with centre OD chord AB.
OD ^ AB
To Prove AD = DB
Const We join OA DOB
Proof In Angle OAD Angle OBD
OA = OB (radii of circle)
OD = OD (Common)
Angle ODA = Angle ODB 90° each (OD ^ AB)
Angle OAD = Angle OBD (RHS Congruency)
AD = DB