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Sub 505 Level|   Geometry|      
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EgmatQuantExpert
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The lengths of two sides in a right-angle triangle other than hypotenu 24 Jul 2019, 01:29
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E
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Difficulty:

5% (low)

Question Stats:

97% (00:47) correct 3% (00:58) wrong based on 118 sessions

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Properties of circles - Practice Question #1

The lengths of two sides in a right-angle triangle other than hypotenuse are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the area of the circle?
A. 5 π
B. 10 π
C. 15 π
D. 20 π
E. 25 π


To read the article: Properties of circles

To read all our articles:Must Read articles to reach Q51

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E
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The lengths of two sides in a right-angle triangle other than hypotenu 24 Jul 2019, 01:33
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EgmatQuantExpert
Properties of circles - Practice Question #1

The lengths of two sides in a right-angle triangle other than hypotenuse are 6 cm and 8 cm. If this right-angle triangle is inscribed in a circle, then what is the area of the circle?
A. 5 π
B. 10 π
C. 15 π
D. 20 π
E. 25 π


To read the article: Properties of circles

To read all our articles:Must Read articles to reach Q51


Length of hypotenuse = \(\sqrt{6^2+8^2} = 10\)

Since diameter of a circle extends right angle on the circumference
hypotenuse is the diameter of the circle = 10
radius = 10/2 = 5
Area of the circle = \(\pi (5)^2 = 25 \pi\)

IMO E
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The lengths of two sides in a right-angle triangle other than hypotenu 24 Jul 2019, 02:06
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So this is a right angled triangle with sides 6 8 and 10.

10 is the diameter.

So area is 25 pi

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The lengths of two sides in a right-angle triangle other than hypotenu 29 Jul 2019, 03:56
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Solution


Given:
    • The lengths of two sides, other than hypotenuse, for a right triangle are 6 cm and 8 cm.
    • This triangle is inscribed in a circle.

To find:
    • Area of the circle

Approach and Working Out:
Let us draw the diagrammatic representation.


By applying the property that angle in a semi-circle is \(90^0\), we can say that AB is the diameter of the circle.
    • And, once we find the length of the diameter, we can find the radius and thus the area of the circle.

Applying the Pythagoras theorem in △ABC,
    • \(AB^2 = AC^2 + BC^2\)
    • \(AB^2 = 6^2 + 8^2 = 36 + 64 = 100\)
    • AB = 10 cm
Since AB is the diameter, AB = 2R = 10
    • Hence, R = 5 cm.
Area of the circle = \(π × R^2 = π × 5^2 = 25π.\)

Hence, the correct answer is option E.

Answer: E

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