Question

1) Length of achord of a circle is 24cm.If distance of the chord from the centre is 5cm,

Find the radius.​

Answer 1

suppose C is the centre of circle

seg AB is chorh

length of AB is 24cm

distance of chord from centre is 5 cm

draw perpendicular from centre to chord AB

the perpendicular drawn from centre of the circle to the chord bisects the chord.

AP = 1/2 x AB

AP = 1/2 x 24

AP = 12 cm

In ∆ APC , L APC = 90°

AC²=AP²+PC²

= 12² + 5²

= 144 +25

AC²= 169

AC =13cm .........taking square root

therefore, the radius of circle is 13 cm

Answer 2

Step-by-step explanation:

GIven AB=24 cm and OC=5 cm 

Since, the perpendicular from the centre of the circle to the chord bisects the chord,

AC=CB=12 cm 

Join, OA, in △AOC

AO2=AC2+OC2(PythagorasTheorem)

=122+562

=144+25=169

⇒AO=169=13cm

∴Diameter=2×=2×AO=2×13cm=26cm