Jambmaths question:
The chord ST of a chord ST of a circle is equal to the radius r of the circle. Find the length of the arc ST.
Option A:
$\tfrac{\pi r}{6}$
Option B:
$\tfrac{\pi r}{2}$
Option C:
$\tfrac{\pi r}{12}$
Option D:
$\tfrac{\pi r}{3}$
Jamb Maths Solution:
$\begin{align} & \text{Triangle SOT is an equilateral triangle since }ST=OS=OT~~ \\ & \text{where }OS\text{ and }OT\text{ are radius of the circle} \\ & \overset{\wedge }{\mathop{Q}}\,=\overset{\wedge }{\mathop{S}}\,=\overset{\wedge }{\mathop{T}}\,\text{ (angle in equiltateral triangle }\!\!\}\!\!\text{ } \\ & \text{Length of the arc}=\frac{\theta }{{{360}^{o}}}\times 2\pi r \\ & =\frac{{{60}^{0}}}{{{360}^{o}}}\times 2\pi r=\frac{\pi r}{3} \\\end{align}$
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