Two parallel chords are drawn on the opposite side of the centre of a
circle of radius 25 cm. If the lengths of the chords are 48 cm and 40
cm reapectively, then find the distance between them.
Answers
Answer:
30 cm
Step-by-step explanation:
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
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