Question

If BC is a diameter of a circle with centre O and OD is perpendicular to the chord AB of a circle, then CA = ____ OD.

___

Answer 1

Given : A circle of centre O, diameter BC and OD perpendicular to chord AB.

Since OD is $\perp$ to chord AB

D is the midpoint of AB (perpendicular drawn from the centre to a chord bisects the chord)

O is the centre

O is the midpoint of diameter BC

In $\Delta$ABC, O and D are the midpoints of BC and AB respectively

OD $\parallel$ AC

OD = $\frac{CA}{2}$

(segment joining the midpoints of two sides of a triangle is half of the third side)

CA = 2OD