turkey-yks 2025 Q39

turkey-yks · Other · yks-ayt Circles Chord Length and Chord Properties

Let $m$ and $n$ be real numbers. In the rectangular coordinate plane, a circle passing through point $A(4, 1)$ is drawn with equation
$$x^{2} + y^{2} - 2x + 6y = n$$
The line $y = mx$ drawn in the plane intersects this circle at points $B$ and $C$. Given that $m(\widehat{BAC}) = 90^{\circ}$, what is the sum $m + n$?
A) 8 B) 9 C) 10 D) 11 E) 12

Let $m$ and $n$ be real numbers. In the rectangular coordinate plane, a circle passing through point $A(4, 1)$ is drawn with equation

$$x^{2} + y^{2} - 2x + 6y = n$$

The line $y = mx$ drawn in the plane intersects this circle at points $B$ and $C$.
Given that $m(\widehat{BAC}) = 90^{\circ}$, what is the sum $m + n$?

A) 8
B) 9
C) 10
D) 11
E) 12

Paper Questions

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