Question

80 is a tangent to a circle at a with Centre O from an external point P such that o t is equals to 8 cm angle OTA is equals to 30 degrees the angle length of AT in centimetres is​

Answer 1

Answer:

Answer:

The length of TA is 2\sqrt{3}cm2

3

cm

Step-by-step explanation:

TA is a tangent to circle at point A. It means the angle OAT is 90 degree because the radius is perpendicular to the tangent at the point of tangency.

So, triangle OAT is a right angle triangle.

\cos\theta=\frac{Base}{Hypotenuse}cosθ=

Hypotenuse

Base

\cos (30^{\circ})=\frac{TA}{4}cos(30

∘

)=

4

TA

\frac{\sqrt{3}}{2}=\frac{TA}{4}

2

3

=

4

TA

\frac{\sqrt{3}}{2}\times 4=TA

2

3

×4=TA

2\sqrt{3}=TA2

3

=TA

Therefore the length of TA is 2\sqrt{3}cm2

3

c