Plane Geometry - Bruce E. Shapiro

252 SECTION 45. EUCLIDEAN CONSTRUCTIONSFigure 45.1: Detail of Raphael’s The School of Athens showing eitherEuclid or Archimedes doing a construction with a compass.4. Circle d intersects −→ AC at P .5. Use the compass to measure the distance BP6. construct a circle k = C(Q, AB).7. Circle k intersects circle h at some point F .8. Then ∠EBF ∼ = ∠BAC.Construction 45.3 (Angle Bisection) Given and angle ∠BAC, find aray −→ AD that bisects ∠BAC.1. Construct a circle c = C(A, r) of any radius centered at A.2. Let P = −→ AC ∩ c and Q = −→ AB ∩ c.3. Use the compass to measure distance P Q.4. Construct circles α = C(P, P Q) and β = C(Q, P Q).5. Let G = α ∩ β (the circles actually intersect at two points, use eitherpoint).Construction 45.4 (Perpendicular Line) Given a line l and a pointA ∈ l, construct a line through A that is perpendicular to l.1. For any radius r, construct circle c = C(A, r).2. Let D and E be the two points where c intersects l.« CC BY-NC-ND 3.0. Revised: 18 Nov 2012