WAEC 2021 · Paper 2 · Q4✱✱

Circle geometry

In the diagram, $AD$ is a diameter of the circle with centre $O$ , $C$ is a point on $AD$ produced, and $BC$ is a tangent to the circle at $B$ . If $\angle OAB = 34^\circ$ , find:

(a)
$\angle OBA$ ;
(b)
$\angle OCB$ .

Worked solution (try it first)

(a)

$|OA| = |OB|$ (radii), so triangle $OAB$ is isosceles.
Its base angles are equal: $\angle OBA = \angle OAB = 34^\circ$ .

(b)

$\angle BOC$ is an exterior angle of triangle $OAB$ , so it equals the sum of the two opposite interior angles: $34^\circ + 34^\circ = 68^\circ$ .
A tangent is perpendicular to the radius at the point of contact, so $\angle OBC = 90^\circ$ .
Angles in triangle $OBC$ : $\angle OCB = 180^\circ - 90^\circ - 68^\circ$
$= 22^\circ$ .

Report a problem with this question