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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

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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Source: Beat The GMAT — Problem Solving | Sat Nov 17, 2018 8:12 pm

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Sun Nov 18, 2018 6:20 am

BTGmoderatorDC wrote:

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

A. 16Ï€
B. 21Ï€
C. 24Ï€
D. 36Ï€
E. 49Ï€
Source: e-GMAT

$$? = \pi {r^2}$$

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

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

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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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 amFollowed by: 34 members; Location: Grand Central / New York; Thanked: 470 times

by Jay@ManhattanReview » Tue Nov 20, 2018 10:18 pm

BTGmoderatorDC wrote:

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

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

Thus, area of âˆ†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 = Ï€*Radius^2 = Ï€*6^2 = 36Ï€

The correct answer: D

Hope this helps!

-Jay
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