DP Further Mathematics HL Questionbank
Angle bisector theorem; Apollonius’ circle theorem, Menelaus’ theorem; Ceva’s theorem; Ptolemy’s theorem for cyclic quadrilaterals.
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- 16M.1.hl.TZ0.11: The points P, Q and R, lie on the sides [AB], [AC] and [BC], respectively, of the triangle ABC....
- 16M.1.hl.TZ0.8b: Let M be any point on \(C\) and N be the \(x\)-intercept of \(C\) between A and B. Prove that...
- 16M.1.hl.TZ0.8a: (i) the value of \(k\); (ii) the radius of \(C\); (iii) the \(x\)-intercepts of \(C\).
- 11M.1.hl.TZ0.5: The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths \(3\) cm and (\9\)...
- 11M.2.hl.TZ0.2b: ABCD is a quadrilateral. (AD) and (BC) intersect at F and (AB) and (CD) intersect at H. (DB) and...
- 10M.2.hl.TZ0.2A.a: By considering (BE) as a transversal to the triangle ACD, show...
- 10M.2.hl.TZ0.2A.b: Determine the ratios (i) \(\frac{{{\rm{AF}}}}{{{\rm{FB}}}}\) ; (ii) ...
- 10M.2.hl.TZ0.2B: The diagram shows a hexagon ABCDEF inscribed in a circle. All the sides of the hexagon are...
- 09M.1.hl.TZ0.3b: AP : PD
- 09M.1.hl.TZ0.3a: AF : FB .
- 09M.2.hl.TZ0.5A: Prove that the interior bisectors of two of the angles of a non-isosceles triangle and the...
- 08M.2.hl.TZ0.3b: A straight line meets the sides (PQ), (QR), (RS), (SP) of a quadrilateral PQRS at the points U,...
- 08M.2.hl.TZ0.3a: The diagram shows the line \(l\) meeting the sides of the triangle ABC at the points D, E and F....
- 07M.2.hl.TZ0.3a: The diagram shows triangle ABC together with its inscribed circle. Show that [AD], [BE] and [CF]...
- 07M.2.hl.TZ0.3b: PQRS is a parallelogram and T is a point inside the parallelogram such that the sum of...
- 12M.1.hl.TZ0.4: The diagram below shows a quadrilateral ABCD and a straight line which intersects (AB), (BC),...
- SPNone.1.hl.TZ0.15a: Prove the internal angle bisector theorem, namely that the internal bisector of an angle of a...
- SPNone.1.hl.TZ0.15b: The bisector of the exterior angle \(\widehat A\) of the triangle ABC meets (BC) at P. The...
- 14M.2.hl.TZ0.9: (a) Show that, with the usual convention for the signs of lengths in a triangle,...
