A circular park has its boundary fenced

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

A circular park has its boundary fenced. Two gates

A

and

B

are located on the fence such that the fence between them subtends an angle of

48^{\circ}

at the centre

O

of the park. A straight walking path is proposed from

A

B

across the park. (i) What is the straight line segment

AB

called with respect to the circle? (ii) Name the region that will be enclosed by the two radii

OA

OB

and the fence between

A

and

B

once the path is constructed. (iii) Name the region that will be enclosed by the straight path

AB

and the fence between

A

and

B

. (iv) Determine the measures (in degrees) of (a) the minor arc

AB

and (b) the major arc

AB

. Show your reasoning clearly.