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If A is the center of the circle shown above and AB = BC

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by BTGmoderatorLU » Wed Dec 12, 2018 3:34 pm

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Source: GMAT Paper Tests

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If A is the center of the circle shown above and AB = BC = CD, What is the value of x?

A. 15
B. 30
C. 45
D. 60
E. 75

The OA is B.
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by Brent@GMATPrepNow » Thu Dec 13, 2018 8:59 am
BTGmoderatorLU wrote:Source: GMAT Paper Tests

Image

If A is the center of the circle shown above and AB = BC = CD, What is the value of x?

A. 15
B. 30
C. 45
D. 60
E. 75

The OA is B.
First recognize that all radii (indicated with BLUE lines) have equal length
Image

Since BC and CD are both equal to the radius AB, we can see that all BLUE lines have equal length
Image

This means the 2 blue triangles are EQUILATERAL triangles, which means all angles = 60°
Image

All we really need answer the question is that these 2 angles are 60° each
Image

This means we have an ISOSCELES triangle with a 120° angle
Image

Since we have an ISOSCELES triangle, the two remaining angles must be 30° each (since all angles must add to 180°
Image

Answer: B

Cheers,
Brent
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by fskilnik@GMATH » Thu Dec 13, 2018 9:59 am
BTGmoderatorLU wrote:Source: GMAT Paper Tests

Image

If A is the center of the circle shown above and AB = BC = CD, What is the value of x?

A. 15
B. 30
C. 45
D. 60
E. 75
ABCD is a rhombus (all sides same length), hence each diagonal bisects the angles at its extremities.

From the fact that angle ABC measures 60 degrees (triangle ABC is equilateral),

? = x = 60/2 = 30 degrees.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
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