Question

A Circle of radius 25 units has a chord going through a point that is located 10 units for the center. What is the shortest possible length that chord could have?

• A. $25units$
• B. $\sqrt{525}units$
• C. $40units$
• D. $\sqrt{2100}units$

Answer 1

The correct option is D $\sqrt{2100}units$

We have a chord going through point that is located 10 units from the centre and radius of circle 25 units.



Here we know
OD = 10 units
AO = 25 units
So by Pythagoras theorem
$AD=\sqrt{A{O}^2-O{D}^2}=\sqrt{{25}^2-{10}^2}=\sqrt{525}$
The line from the centre of the circle divides chord in two equal parts AB = 2CD
$=2\sqrt{525}=\sqrt{4\times 525}=\sqrt{2100}units$