Similarly, AZ = AX and BZ = BY Diameter of circle = 2 x CX = 2 x OY = OX + OY Perimeter of OAB = OA + OB + AB = OA + OB + AZ + BZ = OA + OB + AX + BY = OA + AX + OB + BY = OX + OY = Diameter of circle Marking key/mathematical behaviours Marks Applies result from (b) to establish OX = OY 1 1 Establishes AZ = AX and BZ = BY 1 Determines diameter of circle 1 States perimeter of triangle in terms of the three sides 1 Uses lengths of tangents to establish perimeter of triangle equals diameter of circle Question 2 (a) Let radius of circle be . Since AC = 5 cm, then Marking key/mathematical behaviours Marks Applies length of tangents theorem 1 1 Calculates radius Question 2 (b) Let radius of circle be . Since AC = 13 cm, then Marking key/mathematical behaviours Marks 1 Calculates radius Question 2 (c)
Similarly, AZ = AX and BZ = BY Diameter of circle = 2 x CX = 2 x OY = OX + OY Perimeter of OAB = OA + OB + AB = OA + OB + AZ + BZ = OA + OB + AX + BY = OA + AX + OB + BY = OX + OY = Diameter of circle Marking key/mathematical behaviours Marks Applies result from (b) to establish OX = OY Establishes AZ = AX and BZ = BY Determines diameter of circle States perimeter of triangle in terms of the three sides Uses lengths of tangents to establish perimeter of triangle equals diameter of circle 1 1 1 1 1 Question 2 (a) Let radius of circle be . Since AC = 5 cm, then Marking key/mathematical behaviours Marks Applies length of tangents theorem Calculates radius 1 1 Question 2 (b) Let radius of circle be . Since AC = 13 cm, then Marking key/mathematical behaviours Marks Calculates radius 1 Question 2 (c)