Mathematics · May / June 2020 · Paper 21 · Question 15
0580
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The question as text
A P x° Q B R NOT TO SCALE P, R and Q are points on the circle. AB is a tangent to the circle at Q. QR bisects angle PQB. Angle BQR = x° and x < 60. Use this information to show that triangle PQR is an isosceles triangle. Give a geometrical reason for each step of your work. [3]
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Complete explanation with geometrical reasons [3]
B1 for RQP = x° QR bisects angle PQB
B1 for RPQ = x° alternate segment theorem
B1 for triangle PQR has two equal angles both less than 60 (so can’t be equilateral) so must be isosceles
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