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Home > CBSE > Theorem on Circles CBSE Class IX ICSE Class X (Perpendicular Theorem)

Theorem on Circles CBSE Class IX ICSE Class X (Perpendicular Theorem)

Theorem on Circles CBSE Class IX ICSE Class X (Perpendicular Theorem)

Circles

Theorem!
In a circle a line drawn from centre of a circle ^ to a chord bisect the chord.

Given

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)

By CPCT

AD = DB

Hence Proved!

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