0.5. In a circle of radius 17 cm, two parallel
chords of length 16 cm and 30 cm respectively are
drawn on the same side of the centre. Find the
distance between them
Answers
Answer:
Answer:
The distance between the chords is 23 cm.
Step-by-step explanation:
Let the center of the of the circle is O and radius is 17 cm.
Two parallel chords of length 30 cm and 16 cm are drawn on the opposite side of the center.
Draw altitudes on the cords from the center O. The altitudes divide each of the chord in two equal parts.
Pythagoras theorem: In a right angled triangle
hypotenuse^2=base^2+perpendicular^2hypotenuse
2
=base
2
+perpendicular
2
Use Pythagoras theorem in triangle MOB,
OB^2=MO^2+MB^2OB
2
=MO
2
+MB
2
(17)^2=MO^2+(15)^2(17)
2
=MO
2
+(15)
2
289=MO^2+225289=MO
2
+225
Subtract 225 from both sides.
289-225=MO^2289−225=MO
2
64=MO^264=MO
2
Taking square root on both sides.
8=MO8=MO .... (1)
Use Pythagoras theorem in triangle NOC,
OC^2=NO^2+NC^2OC
2
=NO
2
+NC
2
(17)^2=NO^2+(8)^2(17)
2
=NO
2
+(8)
2
289=NO^2+64289=NO
2
+64
Subtract 64 from both sides.
289-64=NO^2289−64=NO
2
225=NO^2225=NO
2
Taking square root on both sides.
15=NO15=NO .... (2)
The distance between chords is
MN=MO+NOMN=MO+NO
Using (1) and (2)
MN=8+15MN=8+15
MN=23MN=23
Therefore, the distance between the chords is 23 cm.