in the figure, AB and CD are two parallel chords an O is the centre. radius = 15cm. find distance between MN between the two chords of length 24cm and 18cm.
Answers
Answer:
21 cm
Step-by-step explanation:
In the figure, chords AB∥CD
O is the centre of the circle
Radius of the Circle = 15 cm
Length of AB = 24 cm and CD = 18 cm
Join OA and OC
AM = MB = 24/2 = 12 cm
Similarly ON⊥CD
CN = ND = 18/2 = 9 cm
In right △AMO
OA2=OM2+AM2
OM2=OA2−AM2
OM2=152+122=225−144
OM=81=9
Similarly in right △CNO
OC2=CN2+ON2(15)2=(9)2+ON2
225=81+ON2
ON2=225−81
ON=12cm
Now MN=OM+ON=9+12=21cm
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Answer: 21cm
Step-by-step explanation:
In the figure, chords AB∥CD
O is the centre of the circle
Radius of the Circle = 15 cm
Length of AB = 24 cm and CD = 18 cm
Join OA and OC
AM = MB = 24/2 = 12 cm
Similarly ON⊥CD
CN = ND = 18/2 = 9 cm
In right △AMO
OA2=OM2+AM2
OM2=OA2−AM2
OM2=152+122=225−144
OM=81=9
Similarly in right △CNO
OC2=CN2+ON2(15)2=(9)2+ON2
225=81+ON2
ON2=225−81
ON=12cm
Now MN=OM+ON=9+12=21cm