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Practice Exam 1 - GMAT Prep - Geometry

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lucas211 Senior | Next Rank: 100 Posts Default Avatar
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Practice Exam 1 - GMAT Prep - Geometry

Post Wed May 25, 2016 4:19 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Hello BTG

    Would appreciate a little help on the following question:

    Thanks Smile

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    Post Wed May 25, 2016 4:39 pm
    Important: AC is the DIAMETER of the circle.
    Since ∠ABC holds (or contains) the DIAMETER, ∠ABC = 90 degrees.
    So, we have a RIGHT TRIANGLE.

    Side AC is the HYPOTENUSE and it has length 2
    Side BC is a leg and it has length 1
    To find the missing side, we'll us the Pythagorean Theorem:
    1² + (side AB)² = 2²
    1 + (side AB)² = 4
    So, (side AB)² = 3
    So, side AB = √3

    Since we have a RIGHT TRIANGLE, the area = (1/2)(base)(height)
    If we let side AB be the base, then side BC is the height.
    So, the area = (1/2)(√3)(1)
    = √3/2
    = B

    RELATED RESOURCE
    See this video to learn all of the circle properties that the GMAT tests: https://www.gmatprepnow.com/module/gmat-geometry/video/880

    Cheers,
    Brent

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    Post Thu May 26, 2016 6:53 pm
    lucas211 wrote:
    Hello BTG

    Would appreciate a little help on the following question:

    Thanks Smile

    Always remember: A circle inscribed in a semicircle with always be a right angle triangle.
    In this case,
    ∠ABC = 90

    Hence in the triangle ABC, we have base = BC = 1
    Hypotenuse = CA = 2
    Height = AB^2 = 2^2 + 1^2
    Hence AB = √3

    Therefore, area = 1/2*√3*1 = √3/2

    Correct option: B

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