5 Sofia sait que le triangle formé en reliant les villes de Montréal, New York et Paris sur un globe terrestre est semblable à celui qu'on obtient réellement en reliant ces trois villes à vol d'oiseau.
Elle sait que la distance réelle reliant New York et Montréal est de 530 km et que, sur le globe,
le segment reliant ces deux villes mesure 1,3 cm. Si la mesure du segment reliant Montréal
et Paris sur le globe est de 13,5 cm, quelle est la distance réelle entre ces deux villes ?

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12