Question
Question: A wheel of radius 8 units rolls along the diameter of a semicircle of radius 25 units it bumps into ...
A wheel of radius 8 units rolls along the diameter of a semicircle of radius 25 units it bumps into this semicircle. What is the length of the portion of the diameter that cannot be touched by the wheel ?
A
12
B
15
C
17
D
20
Answer
20
Explanation
Solution
AB = Diameter of the bigger circle
= 2(radius) = 2(25) = 50
'C' = Centre of the bigger semicircle.
CQ = 25, PQ = Radius of the smaller circle = 8
CP = CQ – PQ = 25 – 8 = 17
PM = Radius of the smaller circle = 8
CM2 = CP2 – PM2 = 172 – 82
= 289 – 64 = 225 = 152
CM = 15
Similarly, CL = 15.
\ Length of the portion of the diameter of the circle that cannot be touched by the wheel,
AL + MB = AB – (CM + CL)
= 50 – (15 + 15)
= 50 – 30 = 20