E-Math – Geometry – Angle Properties of Circle Source: Mathematics 4, Shinglee, 2014, ex7m, q7

In the diagram, O is the centre of the circle and TA is a tangent to the circle. If 𝐴�̂�𝐵 = 40o, calculate the following angles:

a)𝐴𝑂�𝐶,

b)𝐵�̂�𝐶,

(Angle at centre = 2 x Angle at circumference)

(Angles in opposite segment)

(Angles sum of triangle)

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c) 𝐴�̂�𝑂,

d) 𝑇�̂�𝐵,

(Isosceles triangle)

(Angles in alternate segments)