Math, asked by sumitkash6714, 1 year ago

Two parallel chords of a circle are on the opposite sides of the centre of circle of radius 25cm.if one chord is 48cm long,find the length of the other chord if the distance between the chords is 27cm

Answers

Answered by nickkaushiknick
28

Answer:

30 cm

Step-by-step explanation:

Consider the attached figure in which Two chords AB and CD are given and O is centre of the circle. QP is the distance between two chords

Now, Given that

CD = 48 cm

∴ CQ = 1/2CD              [ Perpendicular from centre bisects a chord]

CQ = 24 cm

OC = 25 cm ( radius)

In ΔOQC

OC² = OQ² + QC²                       [By Pythagoras Theorem]

25² = OQ² + 24²

OQ² = 25² - 24²

OQ² = (25 + 24) ( 25 - 24)          [ ∵ a² - b² = ( a + b) (a - b) ]

OQ² = 49

OQ = 7 cm

Now Distance between chords (QP) = 27 cm

QP = OQ + OP

27 = 7 + QP                                 [∵ OQ = 7 cm ]

QP = 20 cm

In Δ APO

AO² = OP² + AP²                      [By Pythagoras Theorem]

25² = 20² + AP²

AP² = 25² - 20²

AP² = 625 - 400

AP² = 225

AP² = 15²                                  [ ∵ 225 = 15² ]

AP = 15 cm

∵ Perpendicular from centre bisects a chord

∴ AP = PB = 15 cm

AB = AP + PB = 30 cm

∴ Length of other chord is 30 cm

Attachments:
Answered by ankujha693
1

30 cm ......................

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