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