Mathematics · Oct / Nov 2025 · Paper 41 · Question 15
0580
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0580/41/O/N/25 © UCLES 2025 [Turn over 15 NOT TO SCALE ē Ñ C A O 67ã A, Ñ and C lie on a circle, centre O. ēA and ēÑ are tangents to the circle at A and Ñ. Calculate angle AēÑ. Angle AēÑ ¤ [3]
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46 [3]
M2 for [angle ATB] = 180 – 2 × 67 oe OR
M1 for [obtuse] angle AOB = 2 × 67
M1 for angle OAT or angle OBT = 90 OR
M1 for angle TBA = 67 or angle TAB = 67
M1 for angle TDA or TDB = 90 where D is the intersection of OT and AB OR
M1 for angle BOT = 67 or angle AOT = 67
M1 for angle OTB = 180 – 67 – 90 or angle OTA = 180 – 67 – 90
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