Question

The length of perpendicular from the centre on a chord is 1 cm. if the chord subtends the angle at the centre is right angle then what is the length of chord?

Answer 1

From the figure,
OD=1cm
BD=DC(Perpendicular from the center to a chord bisects it)
Angle BOD=Angle DOC=45°
In DOC,
Tan 45=CD/OD
1=CD/1
CD=1cm
As CD=BD and 2CD=BC(Length of the chord)
BC=2cm.
The length of the chord is 2cm.