In the given figure 𝑃𝑄 is chord of length 6 𝑐𝑚 of the circle of radius 6 𝑐𝑚. 𝑇𝑃 and 𝑇𝑄 are tangents to the circle at points 𝑃 and 𝑄 respectively Find ∠𝑃𝑇𝑄.

Given that, 

𝑃𝑄 is chord of length 6 𝑐𝑚 

Radius of the circle is 6 𝑐𝑚 

𝑇𝑃 and 𝑇𝑄 are tangents to the circle at points 𝑃 and 𝑄 respectively 

Now we have to find ∠𝑃𝑇𝑄 

$In ∆𝑃𝑂𝑄, 𝑃𝑄 = 6𝑐𝑚 𝑅𝑎𝑑𝑖𝑖 𝑂𝑄 = 𝑂𝑃 = 6𝑐𝑚$

Here, all sides are equal. So the triangle is an equilateral triangle. 

And also the angles are equal to 60⁰

$\Rightarrow \angle 𝑃𝑂𝑄 = \angle 𝑃 = \angle 𝑄 = 60⁰$

We know that the angle between the tangents of a circle is supplementary to the angle subtended at the centre of the circle 

$\angle 𝑃𝑇𝑄 + \angle 𝑃𝑂𝑄 = 180⁰$

$\angle 𝑃𝑇𝑄 + 60⁰ = 180⁰$

$\angle 𝑃𝑇𝑄 = 120⁰$

Hence, the value of ∠PTQ =120⁰$$\angle PTQ =120⁰$$