Question 9
- PQ is a tangent to a curve RST at the point S. PRT is a straight line, < TPS = 340 and < TSQ = 650.
(i) Illustrate the information in a diagram.
(ii) Find the value of:
- < RTS;
- < SRP.
In the diagram, /VZ/ = /YZ/, <YXZ = 200 and < ZVY = 520. Calculate the size of < WYZ.
Observation
The Chief Examiner reported that this question was not popular among the Candidates’. The reason for this is their inability to draw the diagram and the few that attempted to draw the diagram could not determine the required angles. Thus, Candidates’ performance in this question was reported to be generally poor.
In part (a), Candidates’ were requested to draw circle RST and also a tangent PQ to the circle and then a straight line PRT. They were to locate < TRS = 340 and < TSQ = 650. This is shown as:
Using the knowledge of exterior < of a triangle, then, < RTS = 650 – 340 = 310.
Also, < SRT = 650 ( < in alternate segment) so that < SRP = 1800 – 650 = 1150.
In part (b), the candidates’ were expected to respond as follows:
< XVZ = 1800 – 520 = 1280 (adjacent <s on a straight line)
Therefore, < XZV = 320, < ZVY = <VYZ = 520 (<s in the same segment).
Thus, < WYZ = 520 – 320 = 200.