(a)
In the diagram. \(\over{Rs}\) and \(\over{RT}\) are tangent to the circle with centre O, < TUS = 68\(^o\), < SRT = x and < UTO = y. Find the value of x.
(b) Two tanks A and B are filled to capacity with diesel. Tank A holds 600 litres diesel more than tank B. If 100 litres of diesel was pumped cut of each tank, tank A would then contain 3 times as much as tank B. Find the capacity of each tank.
Explanation
(a). < SOT = 2 < SOT = 2 x 68° =136.
Observe that < OSR = < OTR = 90\(^o\)
So that < OSR + x + < OTR + < SOT = 360\(^o\). Next is to substitute and simplified to get x + 316\(o\) = 360\(o\) so that x = 44\(o\)
(b) If we let capacity of tank A = a and capacity of tank B = b, then
a = 600 + b......(1)
a - 100 = 3(b - 100)
a = 3b - 200........(2)
Substituting (2) into (1) yielded 3b - 200 = 600 + b and solving for b, b = 400.
Therefore. Capacity of tank B = 400litres
Substituting b in (1) yielded A = 600 + 400 = 1000
Capacity of A =1000.