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Chapter 5 Solutions
Elementary Geometry for College Students
- Complete an analytic proof of the following theorem: In a triangle that has sides of lengths a,b, and c, if c2=a2+b2, then the triangle is a right triangle.arrow_forwardd) Let y= Acos2t where A is a constant. Find the value of A such that d? y 3y 9cos2t for all values of t. dr?arrow_forwardSet A A. In OY, BN, BH, and NH are tangents, and NG = 5 cm, HA = 3 cm, and BI = 6 cm. Give what is asked. N G H OY A. 1. Name three points of tangency. HBN 2. HG = Barrow_forward
- = min ||x - p. = min Z(x",P Keung Arts All r i.e. the closest neighbour of p in Euclidean distance is the closest neighbour of p in angle. a opy nghts -Yin Keing A Keng Keun Wai-Yiu Kenngarrow_forwardsolve for carrow_forward(): a The set of points r = in R? such that ||x||, = 1 shows a O A. triangle B. circle O C. square D. none of them E. rhombus (equilateral quadrilateral)arrow_forward
- 4 - find the absolute max. and min. o f the function f = x? +y? on the closed triangle Plate boun ded by the lines x =0 , and 9 + 2 X in the first ニ2 qua drantarrow_forwardIf h1 , h2, and h, are the altitudes dropped from P, Q, and R, respectively, in a triangle (see the figure), show that 1 h2 K where K is the area of the triangle and s = (a + b + c). [Hint: h, = 2K a P C R В aarrow_forwardA. In AABC, D is the midpoint of AB and E is the midpoint of AC. Consider each given information and answer the question that follow using the midline theorem. D B 1. Given that BD = x+6 and AD = 2x+2, what is AB? 2. Given that BC 9x-13, and DE = 3x-2, what is the value of x? 3. Given that DE = 3x+5 and BC = 10x-2, what is the value of x? 4. Given that BC 4x+6 where x = 4, what is DE? 5. Given that EC = x2+6 and AE = 6x-2, what is the value of x?arrow_forward
- ABC is a triangle. BF, CG are any two lines drawn from the extremities of the base BC to meet AC and AB in F and G respectively and intersect in H. Show that AF + AG > HF + HG. CONSTRUCTION: Draw HD and HE || to AB and AC respectively (Fig. G H.arrow_forwarda. In R?, let C be the line segment from (-1,2) to (0,4), and let F = (x + 2, –xy). Evaluate f„F · dř. %3Darrow_forwardProve.arrow_forward
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