Theory question 104
Circle TheoremsIn the diagram, PQRS is a circle with centre O and radius 7cm. SQ and PR intersect at K and ∠SKR = 90°. If the length of the arc SR is four times that of arc PQ, find the length of arc SR. [Take π = 22/7]
Show the model answer
Model answer
The angle between two chords equals half the sum of the arcs they cut off: ∠SKR = ½(arc SR + arc PQ) in degrees.
So arc SR + arc PQ = 180°. With arc SR = 4 × arc PQ: 5 × arc PQ = 180°, arc PQ = 36°, arc SR = 144°.
Length of arc SR = 144/360 × 2 × 22/7 × 7 = 17.6 cm.
Explanation
When two chords cross, the angle between them is half the sum of the two arcs they cut off.