Geometry

2D Coordinate Geometry

2D Coordinate Geometry: Level 4 Challenges

         

What is the area enclosed by (yx)2=4(y-x)^{2}=4 and (y+x)2=4?(y+x)^{2}=4?

The points (3,7),(6,2),(3, 7), (6, 2), and (2,k)(2, k) are the vertices of a triangle. For how many real values of kk is the triangle a right triangle?

Tangents are drawn from P(6,8)P (6,8) to the circle x2+y2=r2x^2+y^2=r^2. Find the radius of the circle such that the area of the triangle formed by tangents and chord of contact is maximum.

Triangle ABC ABC has coodinates A=(4,0)A= (-4, 0), B=(4,0)B= (4 , 0), and C=(0,3)C= (0 , 3).

Let PP be the point in the first quadrant such that ABP\triangle ABP has half the area of ABC\triangle ABC but both triangles have the same perimeter.

What is the length of CP?CP? If your solution is in a form of d\sqrt{d}, submit dd as the answer.

ABCABC is an equilateral triangle such that vertices B,CB,C lie on two parallel lines at a distance of 6 units. If AA lies between the parallel lines at a distance 4 units from one of them, then the length of the side of the triangle is of the form

ABC\large{A\sqrt{\frac{B}{C}}}, where A,B,CA,B,C are co prime natural numbers.

Find A+B+CA+B+C.

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