Points $A$, $B(5, 4)$ and $D$ lie on a circle with centre $C$ and $AB$ is the diameter of

Question

Points $A$, $B(5, 4)$ and $D$ lie on a circle with centre $C$ and $AB$ is the diameter of the circle. The line $y = -x + 9$ is a tangent at point $B(5, 4)$ on the circle. Given that point $P$ lies on $BA$ extended and the $x$-coordinate of point $P$ is $-1$, find the coordinates of $P$.[2] It is given that the distance $BP$ is $3$ times the distance $BC$. Show that centre $C$ is $(3, 2)$.[1] Hence, find the equation of the circle.[2] Given that triangle $BCD$ is a right-angled triangle, find the coordinates of $D$.[3]

Accepted Answer

(a) $P=(-1,-2)$ (b)(i) $C=(3,2)$ (b)(ii) $(x-3)^2+(y-2)^2=8$ (c) $D=(1,4)$

2025 AHS PRELIMS P1 Q11

2025 AHS PRELIMS P1 Q11

Solution:

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