Theory question 104
Surds(a) Without using calculator or mathematical tables evaluate: (3/√3)(2/√3 − √12/6)
(b) In the diagram, O is the centre of the circle. The side AB is produced to E, ∠ACB = 49° and ∠CBE = 68°. Calculate: (i) the interior angle AOC; (ii) angle BOC
Show the model answer
Model answer
(a) 3/√3 = √3 and √12/6 = √3/3. √3 × 2/√3 − √3 × √3/3 = 2 − 1 = 1.
(b)(i) ∠ABC = 180 − 68 = 112°. The reflex angle AOC = 2 × 112° = 224°, so the interior angle AOC = 360 − 224 = 136°.
(ii) ∠BAC = ∠CBE − ∠ACB = 68 − 49 = 19° (exterior angle of triangle ABC). ∠BOC = 2 × 19° = 38°.
Explanation
The angle at the centre is twice the angle at the circumference on the same arc.