A circular park has a radius of

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

Problem

14\,\text{m}

. Two equal straight paths run from the centre

O

of the park to distinct points

A

and

B

on the boundary, making an angle of

90^{\circ}

O

. A low fence is later built along the chord

AB

. (i) Calculate the length of the arc

A\widehat{B}

. (ii) Find the area of the sector

OAB

. (iii) Determine the area of the region of the park that remains inside the fence, i.e. the area of the minor segment cut off by chord

AB