# 4) A circle with centre of O and diameter COB is given if Ab and CD are parasllel then show quad AC is equal to Quad BD.

Your question must be:

A circle with centre O and diameter COB is given. If AB and CD are parallel, then show that chord AC is equal to chord BD.

Given: CB is the diameter of circle with center O. AB and CD are parallel.

To prove: AC = BD

Proof:

We know that angle in a semicircle is a right angle.

So, ∠CAB = ∠BDC = 90°

We also know that the perpendicular distances between two parallel lines are equal.

Since, AB and CD are parallel to each other, so AC = BD.

Hence proved.

Regards

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