# Exam-style Questions: Coordinate Geometry

**1.**

The diagram shows a circular path with centre O and radius r, together with two other paths along the radii AO and OB. The size of the angle AOB is θ radians, where θ < π.

The widths of the paths may be neglected in the calculations. Peter runs along the radii AO and OB, then along the minor arc BA. Mary runs along the major arc AB.

**a)** Given that Peter and Mary run the same distance, show that:

**b)** Given that they each run 410 metres, find the radius of the circular path correct to the nearest metre.

**(Marks available: 5)**

**Answer outline and marking scheme for question: 1**

**Give yourself marks for mentioning any of the points below:**

**a)** Peter's distance = r + r + r Mary's distance = 2 r - r rearranging this gives = - 1

**(2 marks)**

**b)** Rearranging the above equation to show r as a function of gives: This gives a radius of 99m

**(3 marks)**

**(Marks available: 5)**