6. The lengths of two tangent lines to a circle are equal, which can be proved using similar triangles. The perimeter is 2*(3+2+5)=10.
14. c=40 degrees, since c and the given 40 angle correspond to the same arc on the circle. b=40, since b and the given angle are alternate interior angles of two parallel lines. d=180-40-40=100 degrees. a=180-d=180-100=80 degrees.
18. a is two times the given angle according to the inscribed angle theorem. a=2*20=40. b=180-a=140. c=90 since the tangent line is perpendicular to the diameter of the circle.
19. b=85, a=95. Connect the two points on the circle near 45 degrees on the diagram. b is the sum of the two angles formed (b is the exterior angle of the small triangle), and the sum is half the central angles they correspond to, which is 360-145-45=170. So b=170/2=85, and a=180-85=95 degrees.
20. Use power of a triangle. 5*(10+5)=6(6+x), x=6.5.

7 0

3 years ago