Question

# Two  concentric are of radii $$5 cm$$ and $$3cm$$ . Find the length of the chord of the larger circle which touches the smaller circle.

Solution

## Radius of big circle, $$OA = OB = 5cm$$Radius of small circle, $$OP = 3 cm$$Angle between radius and tangent is $$90^{\circ}$$$$\therefore \angle OPA = \angle OPB = 90^{\circ}$$($$\because$$ Chord AB is tangent to small circle )Now , in $$\perp \bigtriangleup OPA, \angle OPA = 90^{\circ}$$$$OP^{2} + AP^{2} = OA^{2}$$$$(3) ^{2} + AP^{2} = (5) ^{2}$$$$9 + AP^{2}= 25$$$$\therefore AP^{2}= 25-9$$$$AP^{2} = 16$$$$\therefore AP = 4 cm$$Similarly , in $$\perp \bigtriangleup OPB , PB = 4 cm$$$$\therefore$$ Length of chord , $$AB = AP + PB = 4 + 4$$$$\therefore$$ chord , $$AB = 8 cm$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More