Question

Find length of a chord of a circle of radius 5 cm two radii are perpendicular to each other

Answer 1

Length of the chord

Answer: required length of the chord is 5√2cm that is 7.071 cm.

Explanation:

Need to find the length of the chord of a circle.

Radius of circle = 5 cm

Also two radii are perpendicular to each other.

Since two radius are perpendicular to each other and third side is chord of a circle . We get a right angled traingle with two sides of 5 cm and hypotenuse that is chord need to be determine.

Consider the attached figure where

O is center of circle . OA and OB represents radii of 5 cm and AB is required CHORD.

On Applying pythagoras theorem on right agled traingle Δ OAB we get

AB² = OA² +OB²      

=> AB² =  5² + 5²

=> AB² = 25 + 25

=>  AB² = 50

=> AB = √50

=> AB = 5√2 = 7.071 cm

Hence required length of the chord is 5√2cm that is 7.071 cm.

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