Question 5 - A-Level Maths

Solve the following inequalities giving your answer in set notation:
1. \(\quad | 4 x + 3 | < | x - 8 |\)
2. \(\quad \frac { x } { x ^ { 2 } + 1 } < \frac { 1 } { 2 }\)
3. If \(a\) and \(b\) are odd integers such that 4 is a factor of ( \(a - b\) ), prove by contradiction that 4 cannot be a factor of \(( a + b )\).
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The diagram shows a circle which passes through the points \(A ( 2,9 )\) and \(B ( 10,3 )\). \(A B\) is a diameter of the circle.
The tangent to the circle at the point \(B\) cuts the \(x\)-axis at \(C\). Find the exact coordinates of \(C\).
Find the exact area of the triangle formed by \(B , C\) and the centre of the circle