(a) Evaluate, without using mathematical tables, \(17.57^{2} - 12.43^{2}\). (b) Prove that angles in the

Explanation

(a) \(17.57^{2} - 12.43^{2}\)

Using the difference of two squares method,

= \((17.57 + 12.43)(17.57 - 12.43)\)

= \((30.00)(5.14)\)

= \(154.2\)

(b)

Given: D and C are points on the major arc of circle ADCB. To prove that < ADB = < ACB.

Construction : Join A and B to O, the centre of the circle .

Proof: With the lettering \(< AOB = 2x_{1}\) (angle at the centre is twice that subtended at the circumference)

But \(< AOB = 2x_{2}\) (the same theorem applies here)

\(\therefore 2x_{1} = 2x_{2} \implies x_{1} = x_{2}\)

\(\therefore < ADB = < ACB\)