wiz-icon
MyQuestionIcon
MyQuestionIcon
3
You visited us 3 times! Enjoying our articles? Unlock Full Access!
Question

In the figure given below, PAB is a secant and PR is a tangent to the circle. If PA : AB = 1 : 8, and PR = 15 cm, find the length of PB.


Open in App
Solution

Given: PAB is a secant and PR is a tangent to the circle.

Also, PA : AB = 1 : 8 and PR = 15 cm.
Let, PA = x. Then AB = 8x
PR = 15 cm

If a chord and a tangent intersect externally, then the product of the lengths of the segmants of the chord is equal to the square of the length of the tangent from the point of contact to the point of intersection.
i.e. (PA)×(PB)=(PR)2

(PA) (PA + AB) = (PR)2 ...[Since, PB = PA + AP]

(x) (x + 8x) = (15)2
(x) (9x) = 225
9x2=225
x2=2259
x2=25
x=5

PA = x = 5 cm
And AB = 8x = 8 x 5 = 40 cm
So, PB = PA + AB = 5 + 40 = 45 cm


flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Intersection between Tangent and Secant
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon