In the xy-plane, the circle C centered at the origin O is intersected

Question

In the xy-plane, the circle C centered at the origin O is intersected by a line l at two points A and B. A line from O is drawn to AB intersecting AB at point D, such that the product of the slopes of OD and AB is -1. If the line l does not pass through origin and the coordinates of point D are (1, -1), what is the radius of the circle?

(1) The x intercept of line l is 2.
(2) The product of the x coordinates of points A and B as well as the

Are You Up For the Challenge: 700 Level Questions

(1) The x intercept of line l is 2.
(2) The product of the x coordinates of points A and B as well as the product of the y coordinates of points A and B is zero.

Are You Up For the Challenge: 700 Level Questions

Superman249 · Answer

IMO: Ans B

Line are perpendicular to each other
as the product of slope is -1

equations:-
One line will be y=(-) x
While other will be y =x-2

D is Perpendicular to AB ; So D will be Perpendicular Bisector of AB

Option 1:- is redundant as we can find from equation of line above that x-intercept will be 2. No result
Not Sufficient

Option 2:- Product of x & y coordinate of A, B is zero means, A & B lies at the axis (either at x & y-axis)

So Coordinate of A or B will be (2,0) & (0,-2)

Here Distance between Origin or either A or B will be radius, Radius will be 2

Sufficient

Hence IMO Ans should be "B"

satya2029 · Answer

Bunuel  Please correct 2nd option

Bunuel · Answer

_______________________________
Fixed. Thank you.

satya2029 · Answer

O(0,0) and D(1,-1)
Slope of OD= -1-0/1-0=-1
Slope of line AB= 1 as OD and AB are perpendicular.
Since both A and B lie on the circle, and OD is perpendicular to AB
D is the mid point of AB, and OA=OB
Since line AB has slope 1, it should be OD distance away from the centre pass through D in such a way that X and Y intercept should be equal as both A and B lies on the circle.
From 1
Radius= X intercept= Y intercept=2
Sufficient
From 2
we know that Slope of line AB is 1
OD= \sqrt{2} 
angle OAD is 45-45-90
OA= 2
Sufficient
D:)

Lipun · Answer

Slope of OD * Slope of AB = -1 => Lines are perpendicular.
OD has a slope of -1, so AB will have a positive slope of 1.
Since, AB passes through (1,-1), thus the X and Y intercepts of AB are 2 and -2 respectively.

ST1: x-intercept of line L is 2. No new info. The coordinates of A and B can be (2,0) and (0,-2) or (3,1) and (-1,-3). In both cases, the x-intercept will be 2.
Not sufficient.

ST2: The product of X-coordinates of A and B as well as the product of Y-coordinates of A and B are both 0. This will only happen if one of the points lies on X-axis and the other lies on Y-axis. A and B lie on the circumference of the circle. From ST1, we know the only possible coordinates of A and B satisfying ST2 are (2,0) and (0,-2). So radius of the circle = 2.
Sufficient.

Ans: B

mahima1811 · Answer

The second statement states that A and B lie on X and Y axis but that doesn't give the value right

For instance it could be 3,-3 too is how I understand it

Would I not need statement 1 to arrive at 2 being the specific value to conclude that 2 is the radius.

So wouldn't it be C instead of B?

Please help me out.

In the xy-plane, the circle C centered at the origin O is intersected

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

In the xy-plane, the circle C centered at the origin O is intersected

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards