Library / UKMT Mathematical Olympiad for Girls /14 of 31

UKMT Mathematical Olympiad for Girls, 2021

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows a quadrilateral $ABCD$ , where $AB$ is $2$ cm and $\angle ABC$ , $\angle ACD$ and $\angle DAB$ are right angles.

(a) Let $E$ be the point on $DA$ such that $CE$ is perpendicular to $DA$ . Prove that triangles $ABC$ and $DEC$ are similar. (2 marks)

(b) Given that the area of quadrilateral $ABCD$ is $6$ cm $^2$ , find all possible values for the perimeter of quadrilateral $ABCD$ . (8 marks)

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.