Question

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

Answer 1

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    

OC^2 = 100 – 64  

OC^2 = 36  

OC = 6 cm  

Distance of the chord from the centre  = 6 cm