Question

there is a circle of radius 5cm and the perpendicular distance from the centre of the circle to the chord of the circle is 3 cm .then ,the length of the chord is

Answer 1

given :-

radius of the circle = 5cm

perpendicular distance from the center to the chord = 3cm

in ∆AOP,

AO = hypotenuse

AP = base

OP = height

by Pythagoras theorem we get,

➡ AO² = AP² + OP²

➡ 5² = AP² + 3²

➡ 25 = AP² + 9

➡ 25 - 9 = AP²

➡ AP = √16

➡ AP = 4cm

now P is bisecting AP since OP is the perpendicular distance between chord and center.

therefore AP × 2 = AB

➡ AB = 4 × 2

➡ AB = 8cm

hence, the length of the chord is 8cm.