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555-605 (Medium)|   Geometry|      
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Bunuel
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If O is the center of the circle shown above and BC=CD, what is the va 17 May 2021, 03:15
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25% (medium)

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80% (01:50) correct 20% (02:01) wrong based on 66 sessions

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If O is the center of the circle shown above and BC=CD, what is the value of x?

A. 15°
B. 20°
C. 25°
D. 30°
E. 40°

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B
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yashikaaggarwal
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If O is the center of the circle shown above and BC=CD, what is the va 17 May 2021, 12:41
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An angle sustended from diameter to any point on circle make 90 degree angle.
Therefore ACD is 90
CAD is 20 (180 degree property)
Since BC and CD are equal.
Both triangles are similar congruent.
Either of ABC or ACB can be 70 & 90 (no need to indulge much)
X will be 20.

Answer is B

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andreagonzalez2k
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If O is the center of the circle shown above and BC=CD, what is the va 17 May 2021, 12:52
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yashikaaggarwal
An angle sustended from diameter to any point on circle make 90 degree angle.
Therefore ACD is 90
CAD is 20 (180 degree property)
Since BC and CD are equal.
Both triangles are similar.
Either of ABC or ACB can be 70 & 90 (no need to indulge much)
X will be 20.

Answer is B

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The answer is B but ABC and ACD triangles are not similar. BAC and CAD angles have same value, but the other four angles of the two triangles have all different values. For example, ABC angle is not a right one but ACD angle is (it can not be a right angle as the cord AC is not the diameter).
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yashikaaggarwal
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If O is the center of the circle shown above and BC=CD, what is the va 17 May 2021, 13:01
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andreagonzalez2k
yashikaaggarwal
An angle sustended from diameter to any point on circle make 90 degree angle.
Therefore ACD is 90
CAD is 20 (180 degree property)
Since BC and CD are equal.
Both triangles are similar.
Either of ABC or ACB can be 70 & 90 (no need to indulge much)
X will be 20.

Answer is B

Posted from my mobile device


The answer is B but ABC and ACD triangles are not similar. BAC and CAD angles have same value, but the other four angles of the two triangles have all different values. For example, ABC angle is not a right one but ACD angle is (it can not be a right angle as the cord AC is not the diameter).
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I never said ABC is right angled. I know it's not. I just kept answer short so it could be solved within a few seconds. Applying the original answers is time consuming process.
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If O is the center of the circle shown above and BC=CD, what is the va 17 May 2021, 13:06
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yashikaaggarwal
andreagonzalez2k
yashikaaggarwal
An angle sustended from diameter to any point on circle make 90 degree angle.
Therefore ACD is 90
CAD is 20 (180 degree property)
Since BC and CD are equal.
Both triangles are similar.
Either of ABC or ACB can be 70 & 90 (no need to indulge much)
X will be 20.

Answer is B

Posted from my mobile device


The answer is B but ABC and ACD triangles are not similar. BAC and CAD angles have same value, but the other four angles of the two triangles have all different values. For example, ABC angle is not a right one but ACD angle is (it can not be a right angle as the cord AC is not the diameter).
I never said ABC is right angled. I know it's not. I just kept answer short so it could be solved within a few seconds. Applying the original answers is time consuming process.
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Sure, but you said "Both triangles are similar." and they aren't.
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If O is the center of the circle shown above and BC=CD, what is the va 17 May 2021, 13:16
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andreagonzalez2k

Sure, but you said "Both triangles are similar." and they aren't.
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Dude, Its congurent. I apologize for misplacing a grave one word.

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If O is the center of the circle shown above and BC=CD, what is the va 12 Jun 2021, 01:57
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yashikaaggarwal
An angle sustended from diameter to any point on circle make 90 degree angle.
Therefore ACD is 90
CAD is 20 (180 degree property)
Since BC and CD are equal.
Both triangles are similar congruent.
Either of ABC or ACB can be 70 & 90 (no need to indulge much)
X will be 20.

Answer is B

Posted from my mobile device
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I have a question here, how are you proving the congruency?
We have no information about the angles of triangle ABC and only two sides of triangle ABC and ACD are equal.

chetan2u Pl. advise!
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If O is the center of the circle shown above and BC=CD, what is the va 12 Jun 2021, 02:35
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RamseyGooner
yashikaaggarwal
An angle sustended from diameter to any point on circle make 90 degree angle.
Therefore ACD is 90
CAD is 20 (180 degree property)
Since BC and CD are equal.
Both triangles are similar congruent.
Either of ABC or ACB can be 70 & 90 (no need to indulge much)
X will be 20.

Answer is B

Posted from my mobile device

I have a question here, how are you proving the congruency?
We have no information about the angles of triangle ABC and only two sides of triangle ABC and ACD are equal.

chetan2u Pl. advise!
Show more

Triangles ABC and ACD are neither similar nor congruent. It is not necessary in order to solve the problem.
As AD is the diameter, angle ACD is 90º. So angle CAD is 20º. And as the inscribed angles CAD and BAC cover the same arc (because CD=BC), they are equal.
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If O is the center of the circle shown above and BC=CD, what is the va 12 Jun 2021, 02:50
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RamseyGooner


I have a question here, how are you proving the congruency?
We have no information about the angles of triangle ABC and only two sides of triangle ABC and ACD are equal.

chetan2u Pl. advise!
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I said triangle to be congruent because they share two sides and one angle.
BC = CD gives one angle equal in both triangle and the AC side is common.
But yes you can go with the arc approach too.
Whatever helps you to keep the approach for this type of question intact.
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If O is the center of the circle shown above and BC=CD, what is the va 12 Jun 2021, 04:37
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RamseyGooner


I have a question here, how are you proving the congruency?
We have no information about the angles of triangle ABC and only two sides of triangle ABC and ACD are equal.

chetan2u Pl. advise!
I said triangle to be congruent because they share two sides and one angle.
BC = CD gives one angle equal in both triangle and the AC side is common.
But yes you can go with the arc approach too.
Whatever helps you to keep the approach for this type of question intact.
Show more


SSA (Side-Side-Angle) condition is not enough to probe that two triangles are congruent (is this case they AREN'T).
https://en.wikipedia.org/wiki/Congruence_(geometry)#Side-side-angle
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If O is the center of the circle shown above and BC=CD, what is the va 12 Jun 2021, 04:48
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andreagonzalez2k
yashikaaggarwal
RamseyGooner


I have a question here, how are you proving the congruency?
We have no information about the angles of triangle ABC and only two sides of triangle ABC and ACD are equal.

chetan2u Pl. advise!
I said triangle to be congruent because they share two sides and one angle.
BC = CD gives one angle equal in both triangle and the AC side is common.
But yes you can go with the arc approach too.
Whatever helps you to keep the approach for this type of question intact.


SSA (Side-Side-Angle) condition is not enough to probe that two triangles are congruent (is this case they AREN'T).
https://en.wikipedia.org/wiki/Congruence_(geometry)#Side-side-angle
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Well, it's mathematics.
The more deeper you go, the more you indulge.
We won't be needing to prove the actual congruency there.
There are always the alternate solutions.

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If O is the center of the circle shown above and BC=CD, what is the va 07 Aug 2025, 02:44
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