Chapter 5 - I’m Up and Down, and Round and Round (Circles)

Math Solutions: Circles, Areas, Probability, and Sequences Chapter 5 - I’m Up and Down, and Round and Round (Circles) Exercise Set 5.1 & 5.2 Q. Draw ΔABC with AB = 5 cm, ∠A = 70° and ∠B = 60°. Draw the circumcircle. Is the centre inside or outside the triangle? Solution: The third angle is ∠C = 180° - (70° + 60°) = 50° . Since all angles are less than 90°, it is an acute-angled triangle. Therefore, the circumcentre lies inside the triangle. Q. What is the least possible radius of a circle passing through two points A and B? Solution: The least possible radius occurs when the segment AB acts as the diameter of the circle. Thus, the minimum radius is AB / 2 . Q. Show that the triangle formed by a chord and the centre of the circle is isosceles. Solution: Let the chord be AB and the centre be O. The sides OA and OB connect the centre to the circumference, so they are radii of the same circle. Hence, OA = OB . Since two sides are equal, ΔOAB is an isosceles triangle …