taiwan-gsat 2023 Q11

taiwan-gsat · Other · gsat__math-b 5 marks Circles Circles Tangent to Each Other or to Axes

On a coordinate plane, there is a circle with center $A(a, b)$ that is tangent to both coordinate axes. There is also a point $P(c, c)$, where $a > c > 0$, and it is known that $\overline{PA} = a + c$. Select the correct options.
(1) $a = b$ (2) Point $P$ is on the line $x + y = 0$ (3) Point $P$ is inside the circle (4) $\frac{a + c}{b - c} = \sqrt{2}$ (5) $\frac{a}{c} = 2 + 3\sqrt{2}$

On a coordinate plane, there is a circle with center $A(a, b)$ that is tangent to both coordinate axes. There is also a point $P(c, c)$, where $a > c > 0$, and it is known that $\overline{PA} = a + c$. Select the correct options.

(1) $a = b$
(2) Point $P$ is on the line $x + y = 0$
(3) Point $P$ is inside the circle
(4) $\frac{a + c}{b - c} = \sqrt{2}$
(5) $\frac{a}{c} = 2 + 3\sqrt{2}$

Paper Questions

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