circle

[Fractal]

i just read that

"when the angle between a chord and a diameter is subtended by an angle between a radius and the same diameter, the measure of the second angle is twice that of the first."

unfortunately, i don't understand this statement. i don't understand why the second angle should always be twice that of the first!

could anybody explain me this statement? thanks a lot

[GMATGuruNY]

i just read that

"when the angle between a chord and a diameter is subtended by an angle between a radius and the same diameter, the measure of the second angle is twice that of the first."

unfortunately, i don't understand this statement. i don't understand why the second angle should always be twice that of the first!

could anybody explain me this statement? thanks a lot

Wow -- I can't remember the last time I used subtended in a sentence. In fact, I can't remember any time.

Here's the rule:

A central angle is formed by 2 radii.
An inscribed angle is formed by 2 chords. (A chord is a line segment with endpoints on the circle.)
When a central angle and an inscribed angle intercept the same arc on the circle, the inscribed angle = 1/2 * the central angle.
Please see the attachment for an illustration.

Hope this helps!

[Fractal]

great explanation, thanks a lot!

this means that if i take two points on a circle and form inscribed angles, this angles
are always the same, right?

[GMATGuruNY]

great explanation, thanks a lot!

this means that if i take two points on a circle and form inscribed angles, this angles
are always the same, right?

Inscribed angles that intercept the same arc will have equal degree measurements. Is this what you're asking?

[Fractal]

Exactly, thank you and sorry for beeing imprecise.