(a) Evaluate, without using mathematical tables, (17.57^{2} – 12.43^{2}).
(b) Prove that angles in the same segment of a circle are equal.
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)