You visited us 1 times! Enjoying our articles? Unlock Full Access!

Intersection between Tangent and Secant

AB and CD are...

Question

AB and CD are two chords of a circle which when produced to meet at a point P such that AB = 5 cm, AP = 8 cm and CD = 2 cm then PD =

12 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

5 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

6 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is B 4 cm
By intersecting secant theorem,
$P A$ $\times$ $P B$ = $P D$ $\times$ $P C$
$8$ cm $\times$ $3$ cm = PD $\times$ (PD+CD)
24 ${c m}^{2}$ = PD $\times$ (PD+2)
${P D}^{2}$ $+ 2 P D - 24 = 0$
On Solving the above quadratic equation, we get
${P D}^{2}$ $+ 6 P D - 4 P D - 24 = 0$
$(P D + 6)$ $\times$ $(P D - 4) = 0$
$P D = 4$ cm & $- 6$ cm
So, $P D = 4$ cm is the real solution

Suggest Corrections

Similar questions

A B

C D

P

C P = 4 c m, A P = 8 c m, P B = 2 c m

P D

A P = 12 c m, A B = 15 c m, C P = P D

C D

A B

C D

P

C P = 4

A P = 8

P B = 2

P D

In the given figure, BOC is a diameter of a circle with centre O. If AB and CD are two chords such that AB||CD and AB = 10 cm then CD = ?

(a) 5 cm

(b) 12.5 cm

(d) 10 cm

Two chords AB and CD of a circle intersect each other at P outside the circle. If AB = 5 cm, BP = 3 cm and PD = 2cm, find CD

Join BYJU'S Learning Program