angle at the circumference

[defeated_soldier]

i dont understand this.....

for a circle what does it mean by "angle at the circumference" ?

How there can be a angle at circumference !!!

I cant visualize the picture. can you help me to understnd this ?

 

[Mrspi]

i dont understand this.....

for a circle what does it mean by "angle at the circumference" ?

How there can be a angle at circumference !!!

I cant visualize the picture. can you help me to understnd this ?

I'm guessing that this terminology is used to refer to an angle whose vertex lies on the circumference of the circle.

There are a couple of possibilities....I'll try to help you see how to draw a diagram to visualize each of them.

1) Draw a circle. Pick any point on the circumference of the circle. Draw two chords in the circle, with each one having your chosen point as one endpoint. NOW, you have an angle with its vertex on the circumference of the circle. The commonly used name for this type of angle is an inscribed angle.

2) Draw a circle. Draw a line which is tangent to the circle (the line and the circle share just one point, and that point is on the circumference of the circle.) Now, use the point of tangency (where the circle and the tangent line "touch") as one endpoint of a chord in the circle. Do you see that the tangent line and the chord form a pair of adjacent angles, each of which has its vertex on the circumference of the circle?

I hope this is what you were looking for.

 

[defeated_soldier]

thanks for the fanatastic explanation.

I think,in my case your first explanation is enough.

because, i am reading this lemma "angle in the centre of a circle is twice the angle at the circumference."

so that means...its pointing to your first explanation.

Thanks again

Regards
defeated_soldier