The diagram shows a circle, centre $O$. Points $A$, $B$, $D$ and $E$ lie on the circle. Th

Question

The diagram shows a circle, centre $O$. Points $A$, $B$, $D$ and $E$ lie on the circle. The line $AD$ is a diameter of the circle and $DCP$ is the tangent of the circle at $D$. The lines $EB$ and $AD$ intersect at point $Q$. The chord $AB$ is produced to meet the tangent $DCP$ at $P$. It is given that $\text{angle}\hspace{0.5em} CBP = \text{angle}\hspace{0.5em} DEB$. Show that $\text{angle}\hspace{0.5em} BCD = 90^\circ$.[4] Show that $DP^2 = BP^2 + DA \times BC$.[4]

Accepted Answer

(a) $\angle BCD=90^\circ$ (shown) (b) $DP^2=BP^2+DA\times BC$ (shown)

2024 CGSS P1 Q13

2024 CGSS P1 Q13

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