What is the radius of the circle?

Expert replies

gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Thu Nov 28, 2013 6:12 pm

Hello,

Can you please assist with this:

In a rectangular coordinate system, circle C has center (0, 0). If point (-4, 4) is on
the circumference of the circle, what is the radius of circle?

(A) 4
(B) 4√2
(C) 4√3
(D) 8
(E) 8√2

OA: B

I was trying to solve as follows:

Length of OC = 4 and length of BC = 4
Hence, CO = CB
Also, angle OCB = 90

So, Triangle OCB = isosceles

Hence, angle OBC = angle BOC = 45

Hence Triangle OCB is a 45 45 90 triangle. So OB = 4.square root of 2

Is this approach correct?

Also, is the slope of line OB be 1 in this case since I am calculating slope as Rise/Run = 4/4 = 1.

Thanks a lot,
Sri

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Source: Beat The GMAT — Problem Solving | Thu Nov 28, 2013 6:12 pm

Uva@90: Master | Next Rank: 500 Posts; Posts: 489; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Nov 28, 2013 7:07 pm

Sri,
You can use distance formula to obtain radius,

Formula is SQRT{(x2-x1)^2 - (y2-y1)^2 }

Here two points are (0,0) and (-4,4)
So,
SQRT{ (-4)^2 + 4^2 } = 4√2

Hence answer is B

Regards,
Uva.

Known is a drop Unknown is an Ocean

Uva@90: Master | Next Rank: 500 Posts; Posts: 489; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Nov 28, 2013 7:12 pm

Sri,
You also did in a correct way only,
You found it is Isosceles Triangle, of angles, 45:45:90
Hence the sides will be in the ratio of

1X:1X:√2X, Here X = 4
So,4:4:4√2

Hence Answer is 4√2

Regards,
Uva.

Known is a drop Unknown is an Ocean

gmattesttaker2: Legendary Member; Posts: 641; Joined: Tue Feb 14, 2012 3:52 pmFollowed by: 8 members; Thanked: 11 times

by gmattesttaker2 » Thu Nov 28, 2013 7:17 pm

Uva@90 wrote:Sri,
You also did in a correct way only,
You found it is Isosceles Triangle, of angles, 45:45:90
Hence the sides will be in the ratio of

1X:1X:√2X, Here X = 4
So,4:4:4√2

Hence Answer is 4√2

Regards,
Uva.

Hello Uva,

Thanks for the explanations. Also is the slope of line OB 1?. In these types of questions I sometimes get confused with whether the length is the same as the slope. Thanks a lot for your help.

Best Regards,
Sri

Uva@90: Master | Next Rank: 500 Posts; Posts: 489; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Thu Nov 28, 2013 7:35 pm

gmattesttaker2 wrote:
Uva@90 wrote:Sri,
You also did in a correct way only,
You found it is Isosceles Triangle, of angles, 45:45:90
Hence the sides will be in the ratio of

1X:1X:√2X, Here X = 4
So,4:4:4√2

Hence Answer is 4√2

Regards,
Uva.

Hello Uva,

Thanks for the explanations. Also is the slope of line OB 1?. In these types of questions I sometimes get confused with whether the length is the same as the slope. Thanks a lot for your help.

Best Regards,
Sri

Hi Sri,
Slope is the measure of Change in Y Axis to the corresponding X axis.

Slope = Y2-Y1 / X2-X1 => 4-0 /-4-0 = -1
Here slope is -1.

Regards,
Uva.

Known is a drop Unknown is an Ocean

theCodeToGMAT: Legendary Member; Posts: 1555; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Thu Nov 28, 2013 9:43 pm

Center is at (0,0)

Using distance formula = sqrt( (4-0)^2 + (-4-0)^2)) ==> sqrt(16+16) ==> sqrt(32) ==> 4 sqrt(2)

R A H U L

Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Fri Nov 29, 2013 9:03 am

The formula for a circle with centre (0,0) is:

x^2 + y^2 = r^2 (or equally use Pythagoras theorem for the triangle)

Substituting x = -4 and y = 4 gives

16 + 16 = r^2

r = √(32) = √(16 * 2) = 4√(2)

So ANSWER (B) 4√2

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