Question

A chords make an angle 120 at the center of the circle of radius 6cm.what is the length of the chord

Answer 1

Answer:

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Answer 2

Chord is $\sqrt 3$ times radius

Step-by-step explanation:

Let AB be the chord subtending a $\angle \theta$ at the centre O of a circle with radius r, as shown in the figure *Attached.

Draw OC⊥AB.

⇒$\angle ACO=90$ and $\angle AOC= \frac {\theta}{2}$

It is given that $\theta =120\ or\ \frac {\theta}{2} =60$

By angle sum property of triangle,

⇒ 30−60−90 triangles, AC = $\frac{\sqrt 3r}{2}$

⇒ AB = 2AC = $\sqrt3 r$

⇒ The length of a chord which subtends an angle of 120 at the center of the circle is $\sqrt 3$ times the radius of the circle.