Cool JEEometry

Geometry Level 5

Let $A$ , $B$ are two points in first quadrant on the line $4x+3y=c$ and $C$ , $D$ are points on positive $x$ -axis and positive $y$ -axis respectively, such that $ABCD$ is a square of side $5$ units. Let the circumcircle of $ABCD$ be $S$ with centre $M(a,b)$ . The find the value of $2a+6b$ .

The answer is 28.

1 solution

คลุง แจ็ค
Jul 24, 2015

Let E and F be two points of intersection on X and Y axis, respectively.

First we can know the coordinates of point C and D because of the slope of linear equation.

hence $C=(3,0) \text{ and }D=(0,4)$

then we only just have to find the coordinate of one of vertex.

Let find the coordinates of B

From the fact that square has 5 units. So the x-coordinate is 7 and y is 3

then we have $(a,b)=\left(\frac{0+7}{2},\frac{4+3}{2} \right)=\left(\frac{7}{2},\frac{7}{2} \right)$

then $2a+6b=(1+3) \times 7=\boxed{28}$

Cool JEEometry

The answer is 28.

1 solution

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