Four benches ,

MATHEMATICS · Multi-part · CBSE · Mathematics · Circles · Circles

Problem

Four benches

P

Q

R

and

S

are placed on the boundary of a circular garden with centre

O

. The benches are arranged so that

\angle POQ=40^{\circ}

\angle QOR=50^{\circ}

and

\angle ROS=30^{\circ}

. (i) Which pair of benches among

PQ

QR

and

RS

are farthest apart and which pair are the nearest? Give reasons for your answer. (ii) If the straight-line distance between benches

P

and

Q

8\,\text{m}

, state with reasons whether the distance between benches

R

and

S

is less than, equal to or greater than

8\,\text{m}

. Explain your conclusion thoroughly.