Theory question 102
Fractions, Decimals and Approximation(a) Evaluate, without using mathematical tables, 17.572 − 12.432.
(b) Prove that angles in the same segment of a circle are equal.
Show the model answer
Model answer
(a) Difference of two squares: (17.57 − 12.43)(17.57 + 12.43) = 5.14 × 30 = 154.2
(b) Diagram: circle centre O, chord AB, points P and Q on the same arc; join OA and OB.
Given: ∠APB and ∠AQB in the same segment. To prove: ∠APB = ∠AQB.
∠AOB = 2∠APB (angle at centre is twice angle at circumference)
∠AOB = 2∠AQB (same reason)
So ∠APB = ∠AQB.
Explanation
For (b), the angle-at-the-centre theorem does all the work; state the reason for each step.