Question

Q.10. 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 centre is 26 cm. If the chord
AB is 16 cm, find its distance from the centre centre ​

Answer 1

Join OB

Line segment joining the center to the tangent is perpendicular to the tangent.

So,

Angle OBP is 90°

Now using Pythagoras theorem,

OB = √(OP^2 - BP^2)

OB = √(26^2 - 24^2) = √(676 - 576) = √100 = 10cm

Now join OD

Line segment joining the center and a chord is the perpendicular bisector of the chord.

So,

DB = 8cm

In ∆ ODB

OD = √(OB^2 - DB^2)

OD = √(10^2 - 8^2) = √(100 - 64) = √36 = 6cm

Therefore, the distance of chord AB from the centre Of is 6cm.