in a circle with centre o and radius 20 cm the chord ab is at a distance of 16cm from centre what is length of chord

Question

in a circle with centre o and radius 20 cm the chord ab is at a distance of 16cm from centre what is length of chord

Answer 1

Sumit,

I wish I could draw you a picture for this. Maybe you could sketch along.

 

Remember that a chord is a line segment that extends from a point on a circle to another point on that circle. And every chord is bisected by the radial line which is perpendicular to it. So if you connect a and b to o, and draw the radial line segment from o to the midpoint of ab, I'll call it P. Now you can see an isosceles triangle with legs = radius = 20 and a base ab, with an altitude oP. Consider 1/2 of that triangle is a right triangle with a hypotenuse of 20 and a leg of 16. We can find the missing leg, aP, using Pythagorean theorem.

 

aP² + 16² = 20²

aP = √(400 - 256) = 12   which is 1/2 of ab.

So ab = 24

 

You might also have recognized the right triangle as a multiple of the standard 3-4-5 right triangle.