Question

AB is a chord of a circle with centre O. At B, a tangent PB is drawn such that its length is 24cm. The distance of P from centre is 26cm. If the chord AB is 16cm, find its distance from the centre.

Answer 1

Since we don't know whether PO bisects AB ... we draw OX perpendicular to AB ... And so we get a Beautiful Right Angled Triangle OAX ✓✓

Answer 2

Given :-

AB is a chord of circle with centre O  and PB = 24 cm, OP = 26 cm.

By Pythagoras theorem,

$\bf\huge OB = \sqrt{(26)^2 - (24)^2}$

$\sqrt{676 - 576}$

$\sqrt{100}$

= 10 cm

Now in ΔOBC

$\bf\huge BC = \frac{16}{2} = 8 cm$

OB = 10 cm

OC^2 = OB^2 - BC^2  

= 100 – 64

OC^2 = 36

OC = 6 cm

Distance of the chord from the centre  = 6 cm