BACCALAURÉAT GÉNÉRAL ET TECHNOLOGIQUE SESSION 2009 ÉPREUVE SPECIFIQUE MENTION « SECTION EUROPEENNE OU DE LANGUE ORIENTALE »
Académies de Paris, Créteil, Versailles Binôme : Anglais / Mathématiques Sujet 5 PLANE GEOMETRY The first part of this page is a summary that can be helpful to do the exercise. A locus is a set of points satisfying a certain condition. For example, the locus of points that are 1cm from an origin is a circle of radius 1cm centred on the origin, since all points on this circle are 1cm from the origin. If a point P is ‘equidistant’ from two points A and B, then the distance between P and A is the same as the distance between P and B, as illustrated here. The locus of points P equidistant from A and B is a straight line called the perpendicular bisector of AB. ×P The plural of locus is loci. Solving triangles Triangles may be solved using the following formulae: a b c = = called the sine rule ; sin A sin B sin C a 2 = b 2 + c 2 − 2bc cos A called the cosine rule.
EXERCISE A, B and C are three points on the coast. Direct distance AB = 80 m, BC = 50 m and AC = 100 m. 1. Construct accurately triangle ABC using a scale of 1 cm to represent 10 m. 2. a) Draw the locus of a point that moves such that it is always the same distance from A and B. b) Draw the locus of a point that moves such that it is always the same distance from B and C. c) Mark the position of a buoy, D, that is the same distance from A, B and C. Draw the circle centre D, radius DA. 3. Another buoy, E, is 30 m away from the straight line joining B and C and 45 m away from D. Find the position of the buoy at E. 4. a) Calculate angle BAC to the nearest degree. b) Deduce, from question a), the size of angle BDC. c) What can you say of triangle BCD ? What is the common distance of D from A, B and C ? Give the answer correct to 3 significant figures. Page : 1/1