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Problem 352

Geometry Difficulty 2.0 Prove it UKMT Senior Kangaroo · United Kingdom · 2024

The triangle $ABC$ is such that $AB = 7$ , $BC = 3$ , and $CA = 5$ . Furthermore, we are given that $\angle ACB = 120°$ . The area of triangle $ABC$ is $M$ . What is the value of $M^2$ , correct to the nearest integer?

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