$A$, $B$ and $C$ are points on a circle, centre $O$. $ACD$ is a straight line, \(\angle BD

Question

$A$, $B$ and $C$ are points on a circle, centre $O$. $ACD$ is a straight line, $\angle BDC=26^\circ$ and $\angle BAO=42^\circ$. Find angle $OBC$. Give a reason for each step of your working.[2] Explain why $BD$ is not a tangent to the circle.[2] As shown, $A,O,C,D$ are collinear; in particular, $AC$ is a diameter.

Accepted Answer

(a) $48^\circ$ (b) $\angle OBD=70^\circ\ne90^\circ$, so $BD$ is not a tangent

2025 AISS PRELIMS P1 Q15

2025 AISS PRELIMS P1 Q15

Solution:

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