DP Further Mathematics HL Questionbank

• Syllabus

2.3

Sub sections and their related questions

Circle geometry.

• 10M.1.hl.TZ0.6a: Show that \(\frac{{{\rm{OR}}}}{{{\rm{OT}}}} = \frac{{{\rm{OT}}}}{{{\rm{OS}}}}\) .
• 10M.1.hl.TZ0.6b: (i)     Show that \({\rm{PR}} - {\rm{RQ}} = 2{\rm{OR}}\) . (ii)     Show...
• 09M.2.hl.TZ0.5B.a: An equilateral triangle QRT is inscribed in a circle. If S is any point on the arc QR of the...
• 09M.2.hl.TZ0.5B.b: Perpendiculars are drawn from a point P on the circumcircle of triangle LMN to the three sides....
• 13M.2.hl.TZ0.6A.a: Show that the opposite angles of a cyclic quadrilateral add up to \({180^ \circ }\) .
• 13M.2.hl.TZ0.6A.b: A quadrilateral ABCD is inscribed in a circle \(S\) . The four tangents to \(S\) at the vertices...
• 13M.2.hl.TZ0.6B.a: Show that the locus of a point \({\rm{P'}}\) , which satisfies...
• 13M.2.hl.TZ0.6B.b: Show that the two tangents to \(C\) from Q are also tangents to \({\rm{C'}}\) .
• 08M.1.hl.TZ0.4a: The triangle ABC is isosceles and AB = BC = 5. D is the midpoint of AC and BD = 4. Find the...
• SPNone.2.hl.TZ0.3a: (i)     Show that CEFB is a cyclic quadrilateral. (ii)     Show that \({\rm{HE}} = {\rm{EP}}\) .
• SPNone.2.hl.TZ0.3b: The line (AH) meets [BC] at D. (i)     By considering cyclic quadrilaterals show that...
• 14M.1.hl.TZ0.9: \({\text{ABCDEF}}\) is a hexagon. A circle lies inside the hexagon and touches each of the six...
• 15M.1.hl.TZ0.13a: Two line segments [\(\rm{AB}\)] and [\(\rm{CD}\)] meet internally at the point \(\rm{Y}\). Given...
• 15M.1.hl.TZ0.13b: Explain why the result also holds if the line segments meet externally at \(\rm{Y}\).
• 16M.2.hl.TZ0.3a: Find the coordinates of the centre of \(C\) and its radius.
• 16M.2.hl.TZ0.3b: Write down the equation of \(C\).
• 16M.2.hl.TZ0.3c: Find the coordinates of the second point on \(C\) on the chord through \((1,{\text{ }}2)\)...
• 18M.2.hl.TZ0.7b.i: Find in terms of R, the two values of (DE)2 such that the area of the shaded region is twice the...
• 18M.2.hl.TZ0.7b.ii: Using two diagrams, explain why there are two values of (DE)2.
• 18M.2.hl.TZ0.7c: A parallelogram is positioned inside a circle such that all four vertices lie on the circle....

Tangents; arcs, chords and secants.

• 15M.1.hl.TZ0.13a: Two line segments [\(\rm{AB}\)] and [\(\rm{CD}\)] meet internally at the point \(\rm{Y}\). Given...
• 15M.1.hl.TZ0.13b: Explain why the result also holds if the line segments meet externally at \(\rm{Y}\).
• 18M.2.hl.TZ0.7b.i: Find in terms of R, the two values of (DE)2 such that the area of the shaded region is twice the...
• 18M.2.hl.TZ0.7b.ii: Using two diagrams, explain why there are two values of (DE)2.
• 18M.2.hl.TZ0.7c: A parallelogram is positioned inside a circle such that all four vertices lie on the circle....

In a cyclic quadrilateral, opposite angles are supplementary, and the converse.

• 18M.2.hl.TZ0.7b.i: Find in terms of R, the two values of (DE)2 such that the area of the shaded region is twice the...
• 18M.2.hl.TZ0.7b.ii: Using two diagrams, explain why there are two values of (DE)2.
• 18M.2.hl.TZ0.7c: A parallelogram is positioned inside a circle such that all four vertices lie on the circle....