Coordinate Geometry
Radical centre of three circles
Grade Class 12
Question:
The radical centre of circles described on the three sides $4x-7y+10=0$, $x+y=5$, and $7x+4y=15$ of a triangle as diameters is
$(-1,2)$
$(1,2)$
$(1,-2)$
$(-1,-2)$
Step-by-Step Solution
Key Concept: The radical centre of three circles with diameters on the sides of a triangle is the orthocentre of the triangle.
Two sides are perpendicular; their intersection $(1,2)$ is the orthocentre = radical centre.
Correct Answer: 2