Motorola M500 Manuel d'utilisateur télécharger pdf (Page 12)

Page 10 M500 180

Problem 180.1 – Two questions about triangles

John Hulbert

Consider a triangle ABC, with point D on AB, and point E on AC, such

that CD = BE. Let F be the point of intersection of CD and BE.

(i) What is the locus of point F as points D and E move along AB and

AC?

(ii) If points D and E are ﬁxed, and line AF extended meets BC at

right angles, is triangle ABC necessarily isosceles?

One of the questions in a physics degree exam at the University of Copen-

hagen was, ‘Describe how to determine the height of a skyscraper with a

barometer.’

One student wrote ‘Tie a long piece of string to the barometer, then

lower it from the roof to the ground. The length of the string plus the

length of the barometer will equal the height of the building.’

Given that Copenhagen is in Denmark and the student won the Nobel

Prize for Physics, who was he? [EK]

‘You need two per cent salt for every kilo of meat . . . ’—Hugh Fearnley

Whittingstall on making salami, Woman’s Hour, BBC R4, 7 Feb 2001.

[Spotted by JRH.]

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Motorola M500 Manuel d'utilisateur Page 12