Mathematics

Mathematics

Problem

In a circle with centre

O

, the chords

AB,\; BC

and

AC

meet at the circumference at points

A,\; B

and

C

. The central angles are given as:

\angle AOB = (3k + 15)^{\circ},\; \angle BOC = (2k + 25)^{\circ},\; \angle AOC = 110^{\circ}

. a. (i) Find the value of

k

. b. (ii) Arrange the chords

AB,\; BC

and

AC

in increasing order of length.

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