Question

1) in the figure C is the center of the circle and CP is perpendicular to the chord AB
CP=5cm and AB=24cm then find
a)The length of AP
b)the radius of the circle ​

Answer 1

GIVEN: A circle with centre O, Radius AO = 13 cm, Chord AB = 24 cm

TO FIND : The perpendicular distance of the chord from O. Let it be called OM.

OM is perpendicular to the chord AB.

Perpendicular from the centre O to a chord bisects the chord. So AM = AB/2 = 12 cm

In right triangle AMO , Using Pythagoras’s Theorem,

AO² = AM² + OM²

=> 13² = 12² + OM²

=> 169 = 144 + OM²

=> OM² = 169 - 144 = 25

=> OM = √25 = 5 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

AO

2

=AC

2

+OC

2

(PythagorasTheorem)

=12

2

+562

=144+25=169

⇒AO=

169

=13cm

∴Diameter=2×=2×AO=2×13cm=26cm