In the diagram, \(\overline{RT}\) and \(\overline{RT}\) are tangent to the circle with centre O. < TUS = 68 ^\circ, < SRT = x, and < UTO = y. Find the value of x.
(b) Two tanks A and B am filled to capacity with diesel. Tank A holds 600 litres of diesel more than tank B. If 100 litres of diesel was pumped out of each tank, tank A would then contain 3 times as much diesel as tank B. Find the capacity of each tank.
Verified Correct Answer: .
Step-by-Step Mathematical Solution
T\(O\)S = 68\(^o\) x 2
= 136\(^o\)
(Angle at centre is twice angle at circumference)
T\(R\) = 180\(^o\) - (90 + 68\(^o\))
= 180\(^o\) - 158\(^o\)
= 22\(^o\)
x = 2 x T\(R\)O = 2 x 22\(^o\) = 44\(^o\)
(b) Let the capacity of Tank B = x litres
Capacity of Tank A = x + 600 litres
If 100 litres is pumoed out of each tank then,
(x + 600) - 100 = 3(x - 100)
x + 500 = 3x - 300
500 + 300 = 3x - x
\(\frac{800}{2} = \frac{2x}{x}\)
x = 400 litres
Capacity of Tank A = 400 + 600
= 1,000 litres
Capacity of Tank B = 400 litres
Source: Myschool Past Questions Archive (Record #58175)