Home
Class 14
MATHS
N is the foot of the perpendicular from ...

N is the foot of the perpendicular from a point P of a circle with radius 7 cm, on a diameter AB of the circle. If the length of the chord PB is 12 cm, the distance of the point N from the point B is

A

`6(5)/(7)cm`

B

`12(2)/(7)cm`

C

`3(5)/(7)cm`

D

`10(2)/(7)cm`

Text Solution

Verified by Experts

The correct Answer is:
D
`angleAPB=90^(@)` (अर्धवृत्त का कोण समकोण होता है)
`therefore DeltaAPB` में,
`AP^(2)+PB^(2)=AB^(2)`
`implies AP^(2)+12^(2)=14^(2)`
`implies AP^(2)=196-144=52`
`implies AP=sqrt(52)`
AN = x (मान लिया), `therefore NB=(14-x)`
`DeltaAPN` में
`AP^(2)=AN^(2)+PN^(2)`
`implies 52=x^(2)+PN^(2)` `implies PN^(2)=52-x^(2)`
`DeltaPNB` में,
`implies PB^(2)=PN^(2)+(14-x)^(2)`
`implies 144=52-x^(2)+(14-x)^(2)`
`implies 92=-x^(2)+196+x^(2)-28x`
`implies 196-92=28x`
`implies x=(104)/(28)`
`therefore BN=14-x=14-(104)/(28)=14-(26)/(7)`
`therefore BN=(98-26)/(7)=(72)/(7)=10(2)/(7)cm`
Promotional Banner

Similar Questions

Explore conceptually related problems

The radius of a circle is 8cm and the length of one of its chords is 12cm. Find the distance of the chord from the centre.

The radius of a circle is 10cm. The length of a chord is 12 cm. Then the distance of the chord from the centre is "__________________" .

The length of the tangent from an external point P to a circle of radius 5cm is 10cm . The distacne of the point from the centre of the circle is

Distance of chord AB from the centre of a circle is 8 cm.12 cm. Length of the chord AB is 12 cm. Find the diameter of the circle.

A) The radius of a circle is 5 cm. At this point The tangent is drawn if the length of the tangent is 12 cm. Find the distance from the center of the circle to the point.