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Fractal: Master | Next Rank: 500 Posts; Posts: 183; Joined: Sun Aug 22, 2010 1:02 am; Location: Switzerland; Thanked: 5 times

circle

by Fractal » Sat Sep 18, 2010 1:52 am

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

Quote

Source: Beat The GMAT — Problem Solving | Sat Sep 18, 2010 1:52 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sat Sep 18, 2010 5:18 am

Fractal wrote: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!

Attachments

BTG_inscribed_angle.pdf: (47.39 KiB) Downloaded 110 times

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Fractal: Master | Next Rank: 500 Posts; Posts: 183; Joined: Sun Aug 22, 2010 1:02 am; Location: Switzerland; Thanked: 5 times

by Fractal » Sat Sep 18, 2010 9:15 am

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?

Quote

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pm; Location: New York, NY; Thanked: 13060 times; Followed by:1906 members; GMAT Score:790

by GMATGuruNY » Sun Sep 19, 2010 2:38 am

Fractal wrote: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?