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This is how I am trying to solve this, but there is bit of a guess work. So can someone please help?

Considering the figure CD is the diameter of the circle and its the hypotenuse of the triangle too i.e. Angle CBD= 90 degrees. --------------------------------------(1). This is where I am guessing.

If that's the case then considering statement 1

Knowing that the side ratios of the 30:60:90 degree triangle are 1:\(\sqrt{3}\):2 the know that the x = 30 and y = 60 as the x is the angle opposite to the shortest leg. Therefore, sufficient.

Re: Is angle x = 30 degrees? [#permalink]
05 Feb 2012, 17:01

Expert's post

Attachment:

Triangle.jpg [ 13.63 KiB | Viewed 3782 times ]

If CD is the diameter of the circle, does x equal 30?

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.

So, angle CBD is a right angle.

(1) The length of CD is twice the length of BD --> ratio of a hypotenuse to a side is 2:1 --> we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient.

Re: Is angle x = 30 degrees? [#permalink]
05 Feb 2012, 17:05

enigma123 wrote:

If CD is the diameter of the circle, does x equal 30?

(1) The length of CD is twice the length of BD. (2) y = 60

This is how I am trying to solve this, but there is bit of a guess work. So can someone please help?

Considering the figure CD is the diameter of the circle and its the hypotenuse of the triangle too i.e. Angle CBD= 90 degrees. --------------------------------------(1). This is where I am guessing.

Hi,You are right in your logic. In fact what you are guessing is actually true ,with respect to the figure-- If the hypotenuse of the triangle is also the diameter of the circle , then the angle opposite to it is a right angle . In other words 'the angle inscribed by the diameter of a circle is a right angle'. _________________

Rules for posting on the verbal forum When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources such as 1000 series.

Rules for posting on the verbal forum When you post a question Pls. Provide its source & TAG your questions Avoid posting from unreliable sources such as 1000 series.

Re: Is angle x = 30 degrees? [#permalink]
27 Feb 2014, 04:52

Bunuel wrote:

Attachment:

Triangle.jpg

If CD is the diameter of the circle, does x equal 30?

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.

So, angle CBD is a right angle.

(1) The length of CD is twice the length of BD --> ratio of a hypotenuse to a side is 2:1 --> we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient.

(2) y = 60. x=180-90-60=30. Sufficient.

Answer: D.

I am having difficulties applying ratios in triangles. If CD=2BD then the their ratio is (CD/BD)= 2. Based on this, shouldn't the ratio of their corresponding angles (90° corresponds to side CD, and x° corresponds to BD) be the same? So, (90°/x°)=2 --> x°=45° I know this is wrong, and I understand the explanation using the 30-60-90 ratio but I don't understand why my ratio lead to the wrong solution. I hope someone can clarify this for me

Re: Is angle x = 30 degrees? [#permalink]
27 Feb 2014, 05:21

Expert's post

damamikus wrote:

Bunuel wrote:

Attachment:

Triangle.jpg

If CD is the diameter of the circle, does x equal 30?

A right triangle inscribed in a circle must have its hypotenuse as the diameter of the circle. The reverse is also true: if the diameter of the circle is also the triangle’s hypotenuse, then that triangle is a right triangle.

So, angle CBD is a right angle.

(1) The length of CD is twice the length of BD --> ratio of a hypotenuse to a side is 2:1 --> we have 30°, 60°, and 90° right triangle, where the sides are always in the ratio \(1:\sqrt{3}:2\). BD corresponds with 1, thus it's smallest side and opposite the smallest angle (30°). Sufficient.

(2) y = 60. x=180-90-60=30. Sufficient.

Answer: D.

I am having difficulties applying ratios in triangles. If CD=2BD then the their ratio is (CD/BD)= 2. Based on this, shouldn't the ratio of their corresponding angles (90° corresponds to side CD, and x° corresponds to BD) be the same? So, (90°/x°)=2 --> x°=45° I know this is wrong, and I understand the explanation using the 30-60-90 ratio but I don't understand why my ratio lead to the wrong solution. I hope someone can clarify this for me

cheers,

Max

In a triangle the ratios of the sides and the ratios of the angles not necessarily equal to each other. _________________

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