Theory question 112
Number Bases(a) Simplify √1001two, leaving your answer in base two.
(b) In the diagram, O is the centre of the circle radius x. |PQ| = z |OK| = y and ∠OKP = 90°. Find the value of z in terms of x and y
Show the model answer
Model answer
(a) 1001two = 8 + 1 = 9, and √9 = 3 = 11two.
(b) OK ⟂ PQ, so K is the midpoint of PQ and KP = z/2.
In right-angled triangle OKP: (z/2)2 + y2 = x2, so z = 2√(x2 − y2).
Explanation
A perpendicular from the centre bisects the chord.