MyQuestionIcon

1

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

A Line through the Center That Bisects the Chord Is Perpendicular to the Chord.

Two chords AB...

Question

Two chords AB and CD of a circle intersect each other at P outside the circle. If AB = 6 cm, BP = 2 cm and PD = 2.5 cm, find CD.

Open in App

Solution

ANSWER:
AB and CD are two chords of a circle which intersect each other at P outside the circle.
AB = 6 cm, BP = 2 cm and PD = 2.5 cm
∴ AP × BP = CP × DP
⇒ 8 × 2 = (CD + 2.5) × 2.5 [∵ CP = CD + DP ]
Let CD = x cm
Thus, 8 × 2 = (CD + 2.5) × 2.5
⇒ 16 = 2.5 x + 6.25
⇒ 2.5x = (16 - 6.25) = 9.75
⇒ x=9.752.5=3.9
Hence, CD = 3.9 cm

Suggest Corrections

thumbs-up

32

Similar questions

A B

C D

of a circle intersect each other at

P

outside the circle. If

A B = 6 c m, B P = 2 c m

P D = 2.5 c m

C D

.

A B

C D

of circle intersect at

P

A P = 12 c m, P B = 6 c m

C P = 2 c m

, the length of

P D

A B

C D

are two chords of a circle which intersect each other internally at

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

of a circle when produced meet outside the circle at P. If

A B = 4

B P = 3

C P = 14

cm, then the length of

C D

A B

C D

of a circle intersect each other (externally) at

P

outside the circle. If

A P = 10

C P = 6

P D = 5

P B

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Circles and Their Chords - Theorem 4

MATHEMATICS

Watch in App

explore_more_icon

Explore more

A Line through the Center That Bisects the Chord Is Perpendicular to the Chord.

Standard IX Mathematics

Join BYJU'S Learning Program

CrossIcon