Shape and Space 6
4 marks · NormalAB and CD are two chords of a circle, intersecting at point P inside the circle. AP = 3 cm, PB = 6 cm, CP = 4 cm.
(a)[2 marks]
Find the length of DP.
(b)[2 marks]
State and use the relevant circle theorem.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
Show answer
(a) 4.5 cm
(b) AP × PB = CP × DP, so 3 × 6 = 4 × DP
Common mistakes: Not using chord theorem; Not multiplying correctly
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · States/interprets AP × PB = CP × DP.
A1 (a) · 1 mark · Gets DP = 4.5 cm.
B1 (b) · 2 marks · Names the intersecting chords theorem with correct relation.
Worked solution
Intersecting chords theorem: AP × PB = CP × DP.