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/sci/ - Science & Math

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File: 50 KB, 607x610, plz-halp.jpg [View same] [iqdb] [saucenao] [google]
3209450 No.3209450 [Reply] [Original]

I'm studying and my brain is turned off today. I'd love someone to explain how it's established that the marked angle is 2α.

In the picture the black box is the question, and lower half is the solution.

>> No.3209459

Also I failcropped the image so 4.(c) (ii) is irrelevant, I got that part fine.

tnq

>> No.3209460

Probably a property of triangles inscribed into semicircles.

>> No.3209462

The angle doubles because triangle acb is a right triangle.

>> No.3209466

Thank you, I got it and looked up to see my first response was the answer. Isosceles and I used to be good friends but we've fallen out over the past few years

>> No.3209471

>>3209462
Not correct or even a good explanation my friend, but thanks for the input

>> No.3209483
File: 41 KB, 609x355, cicrle geometry.jpg [View same] [iqdb] [saucenao] [google]
3209483

thats just how circles work. hopefully this image explains it.

>> No.3209491

>>3209450

Studying for Paper II on monday? That's 2007 Q4 (c)(ii) right?
I did this this morning but I'm really too lazy to help you..

>> No.3209495
File: 264 KB, 458x355, zx5.png [View same] [iqdb] [saucenao] [google]
3209495

>>3209483
the reason [bac] and [aco] mjust be teh same is that any sector of a circle from the origin, must be an iscoceles triangle (or equilateral perhaps..) but the point is that isosceles triangle has 2 angles that are the same, so we know the otehr angle MUST be α as well.
the rest is obvious if you know angles in a triangle = 180 degrees, and angles in a straight line = 180 degrees.
hopefully you can follow the picture.

>> No.3209508

>>3209471
Really? It seems to me if you take any right triangle and draw a line connecting angle c to the exact center of the hypotenuse, then the angle you get will always will be twice angle a. I may very well be retarded though.

>> No.3209526

if you take a certain arc length ("pie crust") of the circle, and draw an inscribed (vertex on the circumference of the circle) angle containing that arc length, and a central (vertex at the center of the circle) angle containing that same arc length, the central angle will always be 2 times the inscribed angle.

look up central and inscribed angles for a more detailed explanation

>> No.3209536

Thank you sci, I've decided if this question comes up on my exam to deduce that the angle is 2α because that's just how circles work

>> No.3209540

>>3209508

what you are describing is the median of a triangle, which is not the same thing as the angle bisector (except in a rare cases).

http://www.cliffsnotes.com/study_guide/Altitudes-Medians-and-Angle-Bisectors.topicArticleId-18851&#4
4;articleId-18787.html

>> No.3209544

>>3209450
triangle aoc is isoceles, because ao = oc = r
thus angle aco = angle oac = alpha
so angle aoc = 180 - alpha - alpha
and angle boc = 180 - aoc = 180 - (180 - alpha - alpha) = 2*alpha

(from there, you can show that triangle boc is isoceles, so angle ocb = 90 - alpha, so angle acb = alpha + (90-alpha) = right angle)

>> No.3209552

>>3209495
EK could you stop posting that blond girl
she really bugs me out
there's something in her that really irritates me
thanks in advance

>> No.3210876

>>3209450
hint: oc = ob (length)

>> No.3210883

>>3209552
bugs you out?
wtf? why?