Question

Radius of a circle is 20cm . Distance of a chord from the centre of the circle is 12 cm . Find the length of the chord ​

Answer 1

Answer

32cm

Step-by-step explanation:

Given - A circle with center O and chord CD

Radius (OC=OD) = 20 cm

Perpendicular distance (OP) = 12 cm

So, in the right triangle OPD, By Pythagoras Theorem,

OD square = OP square + PD square

20 square = 12 square + PD square

400 = 144 + PD square

256 = PD square

16 = PD

Similarly, PC = 16 cm

So, Chord CD = PD + PC = 16 +16 = 32cm.

Answer 2

Answer:

length of the Chord = 32 cm

Step-by-step explanation:

Given radius of circle is 20 cm

distance of chord from center of circle = 12 cm

length of the  chord = 2 × $\sqrt{ r^{2}-d^{2} }$   (  r = radius, d= perpendicular distance

                                   = 2 × $\sqrt{20^{2} -12^{2} }$         of chord center of the from circle )  

                                   = 2 × $\sqrt{400 -144}$

                                    = 2 × $\sqrt{256}$

                                    = 2( 16) = 32 cm