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Geometry: Circles

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Geometry: Circles

by Yaj » Thu Sep 12, 2013 2:49 am
Some help:

In the figure above, is angle DAB = angle DCB?
(1) Angle ADC is twice angle ABC
(2) BD is twice the radius of the circle.

[spoiler]OA: B[/spoiler]

Thank You!
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by vinay1983 » Thu Sep 12, 2013 3:34 am
Statement 1

We only know that the 2 angles are related to one another.if one angle is 10, other angle is 20 or vice versa.

Statement 2

It say's that BD is "twice" the radius.This is nothing but the diameter, hence 2 right angles will be created since diameter of a circle is the hypotenuse of the right angle triangle.

Right angle triangle ABD and BDC

So both angles angle DAB and Angle DCb are 90 degrees and hence equal.

I hope I am right!
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by vinay1983 » Thu Sep 12, 2013 3:36 am
Yaj wrote:Some help:

In the figure above, is angle DAB = angle DCB?
(1) Angle ADC is twice angle ABC
(2) BD is twice the radius of the circle.

[spoiler]OA: B[/spoiler]

Thank You!
Further my query is what if a central angle is introduced in option A instead of the present one.Will then A be sufficient?
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by ceilidh.erickson » Thu Sep 12, 2013 12:52 pm
Vinay, you're absolutely correct. We know that the sum of the angles in a quadrilateral will be 360 degrees, but knowing that two of the angles are x and 2x doesn't help us to know anything about the other two.

The second statement tells us that BD is the diameter of the circle. If we drew that diameter, it would create two inscribed triangles that both have the diameter as a side length. When that's true, they both have to be right angles, and thus equal.

I'm not sure what you mean in your question about central angles. If which angles were central angles?
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