(a)
In the diagram, A, B, C and D are points on the circumference of a circle. XY is a tangent at A. Find : (i) < CAX ; (ii) < ABY.
(b) If (m + 1) and (m – 3) are factors of (m^{2} – km + c), find the values of k and c.
Explanation
(a) (< ADB = < ACB = 20°) (Angle in the same segment).
In (Delta ACY),
(hat{C} = < ACB)
(i) (hat{C} + hat{A} + hat{Y} = 180°)
(20° + hat{A} + 60° = 180°)
(hat{A} = 180° – 80° = 100°)
(< CAY = hat{A} = 100°)
(< CAX = 180° – 100° = 80°)
(ii) In (Delta ACB),
(hat{B} = hat{C} = frac{180° – 20°}{2} )
= (frac{160°}{2})
= (80°)
In (Delta ABY),
(< ABY = hat{B} = 180° – 80°)
= (100°)
(b) ((m + 1)(m – 3) equiv m^{2} – km + c)
(m^{2} – 3m + m – 3 = m^{2} – 2m – 3)
(m^{2} – 2m – 3 equiv m^{2} – km + c)
(implies k = 2 ; c = -3)