Problem Solving

The area=(3x9)/2-(3*1)/2=(3(9-1))/2=12

Mike@Magoosh wrote:Point W = (5, 3). Circle J has a center at point W and radius of r = 5. This circle intersects the y-axis at one intercept and the x-axis at two intercepts. What is the area of the triangle formed by these three intercepts?
(A) 7.5
(B) 12
(C) 15
(D) 24
(E) 30

This question is medium difficulty. If you would like to practice on a set of medium to very hard problems on Coordinate Geometry, as well as see the OE of this question, see:
https://magoosh.com/gmat/2014/challengin ... questions/

OA = [spoiler](B)[/spoiler]

Mike

Equation of Circle with Radius 5 units and center at (h,k) => (X-h)^2 + (Y-k)^2 = 5^2
i.e. (X-5)^2 + (Y-3)^2 = 25

This circle intersects the y-axis at one intercept which mean the Circle is Tangent to the Y-Axis

For point of Intersection at Y-Axis, X = 0

Substitute it in the Equation of Circle
i.e. X^2 + Y^2 = 25 ===> i.e. (-5)^2 + (Y-3)^2 = 25
i.e. Y = 3

For X-Intercepts of the Circle, Y = 0
i.e. (X-5)^2 + (Y-3)^2 = 25 ===> (X-5)^2 + (0-3)^2 = 25 ===> (X-5)^2 = 16
i.e. X-5 = +4 ===> i.e. X = 9, 1

Therefore Point of Intersections are (9,0) (1,0) and (0,3)
This is a triangle with Base as Distance between (9,0) and (1,0) = 8
and Height as Y-coordinate of point (0,3) = 3
Therefore Area of Triangle = (1/2) x 8 x 3 = 12

Answer: Option D