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In the given diagram, the circle touches the y-axis at the

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by BTGmoderatorDC » Sat Nov 17, 2018 8:12 pm

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$$In\ the\ given\ diagram,\ the\ circle\ touches\ the\ y-axis\ at\ the\ point\ K\ whose\ coordinate\ is\ (0,7).$$
$$If\ the\ area\ of\ triangle\ CKO\ is\ 21\ units^2,\ where\ C\ is\ the\ center\ of\ the\ circle,\ find\ the\ area\ of\ the\ circle.$$

A. 16Ï€
B. 21Ï€
C. 24Ï€
D. 36Ï€
E. 49Ï€

OA D

Source: e-GMAT
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by fskilnik@GMATH » Sun Nov 18, 2018 6:20 am
BTGmoderatorDC wrote:Image

$$In\ the\ given\ diagram,\ the\ circle\ touches\ the\ y-axis\ at\ the\ point\ K\ whose\ coordinate\ is\ (0,7).$$
$$If\ the\ area\ of\ triangle\ CKO\ is\ 21\ units^2,\ where\ C\ is\ the\ center\ of\ the\ circle,\ find\ the\ area\ of\ the\ circle.$$

A. 16Ï€
B. 21Ï€
C. 24Ï€
D. 36Ï€
E. 49Ï€
Source: e-GMAT
$$? = \pi {r^2}$$

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$${{7 \cdot r} \over 2} = 21\,\,\,\,\, \Rightarrow \,\,\,\,\,r = 2 \cdot 3\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 36\pi $$


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

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Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by Jay@ManhattanReview » Tue Nov 20, 2018 10:18 pm
BTGmoderatorDC wrote:Image

$$In\ the\ given\ diagram,\ the\ circle\ touches\ the\ y-axis\ at\ the\ point\ K\ whose\ coordinate\ is\ (0,7).$$
$$If\ the\ area\ of\ triangle\ CKO\ is\ 21\ units^2,\ where\ C\ is\ the\ center\ of\ the\ circle,\ find\ the\ area\ of\ the\ circle.$$

A. 16Ï€
B. 21Ï€
C. 24Ï€
D. 36Ï€
E. 49Ï€

OA D

Source: e-GMAT
To get the area of the circle, we need the value of its radius.

Since the circle touches Y-axis at point K, Y-axis would be a tangent to the circle and CK would be the radius.

Thus, ∆OCK is a right-angled triangle with OK is its bases and CK is its altitude (height).

Thus, area of ∆OCK = 1/2*OK*CK

=> 21 = 1/2*7*CK; note that OK is y coordinate of the point K.

=> CK = Radius of the circle = 6 units

Thus, area of the circle = π*Radius^2 = π*6^2 = 36π

The correct answer: D

Hope this helps!

-Jay
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