Question

AC is a chord and BC Is a diameter at a circle having O as centre. If OD is perpendicular to AC,then prove:AB=2OD

Answer 1

1] Side BC is a diameter. O divides BC into two equal parts. OB = OC = radius.
2] Perpendicular on a chord from the centre of the circle is perpendicular bisector of the chord. So, AD = DC.
3] In triangle (ABC) and triangle (DOC) , Angle C is common.

So, By SAS test, these two triangles are similar.
Therefore, AB/DO = AC/DC = BC/OC.
Since, AC/DC = BC/OC = 2
AB/DO =2
Therefore, AB = 2DO = 2OD.