Shape and Space 6
4 marks · NormalIn the diagram, OA and OB are radii of the circle, centre O. TB is a tangent to the circle at point B. Angle OBA = 68°.
Work out the size of angle ABO.
Find the size of angle OAB.
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(a) 22 °
(b) 22 °
Common mistakes: Not recognising radii are equal; Forgetting angle sum in triangle
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Uses triangle OAB, noting two sides are radii.
A1 (a) · 1 mark · Finds ABO = 22°.
M2 (b) · 1 mark · Notes two equal angles at base of isosceles triangle.
A2 (b) · 1 mark · Finds OAB = 22°.
Worked solution
Triangle OAB has two sides equal (radii OA = OB), so angles ABO and OAB are equal.
Angle BOA is between the radii, at the centre. However, angle OBA is between the radius OB and tangent TB at B, which is 90°. Given OBA = 68°, so angle ABO in triangle OAB is (180 − 90 − 68) = 22°.