A safe distance should be maintained so that sufficient time and space are available to react and stop safely if the truck suddenly applies its brakes. The required distance depends on speed, reaction time, and braking conditions.
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∠MOP is the angle subtended by arc MP at the centre, while ∠MNP is subtended by the same arc at the circumference. Therefore, the central angle is twice the angle at the circumference.
Each side of a regular hexagon subtends 60° at the centre. The triangle formed is equilateral, so each side is r. The distance from the centre to each side is (√3/2)r.
Half of the chords are 5 cm and 12 cm. Let the distance of the 24 cm chord from the centre be x. Then the other is x + 7. Solving gives x = 5 and radius = 13 cm.
Since AB and AC are congruent chords, they are equidistant from O. In triangles AOB and AOC, OA is common and OB = OC. Hence, the triangles are congruent, giving ∠BAO = ∠OAC. Therefore, AO bisects ∠BAC.