Question

Bookwork code: M29 Calculator allowed The circle below has centre U. BC and DE are tangents to this circle. Work out the size of angle 0. Give reasons for your answer. A 52° B O E Watch video D 27° 0 C Not drawn accurately A Bookwork code : M29 Calculator allowed The circle below has centre U. BC and DE are tangents to this circle . Work out the size of angle 0 . Give reasons for your answer . A 52 ° B O E Watch video D 27 ° 0 C Not drawn accurately A​

Answer 1

1) $OA=OB$ (all radii of a circle are equal)

2) $\angle OBA=52^{\circ}$ (angles opposite equal sides in a triangle are equal)

3) $\angle OAB+\angle OBA+\angle AOB=180^{\circ}$ (angles in a triangle add to 180 degrees)

4) $52^{\circ}+52^{\circ}+\angle AOB=180^{\circ}$ (substitution)

5) $\angle AOB=76^{\circ}$ (subtraction)

6) $\angle AOB+\angle BOD=180^{\circ}$ (angles on a line add to 180 degrees)

7) $76^{\circ}+\angle BOD=180^{\circ}$ (substitution)

8) $\angle BOD=104^{\circ}$ (subtraction)

9) $\angle ODE=\angle OBC=90^{\circ}$ (tangents are perpendicular to the radius of a circle at the point of tangency)

10) $\angle ODC=117^{\circ}$ (angle addition postulate)

11) $\angle BOD+\angle OBC+\angle ODC+\angle DCB=360^{\circ}$ (angles in a quadrilateral add to 360 degrees)

12) $104^{\circ}+90^{\circ}+117^{\circ}+\theta=360^{\circ}$ (substitution)

13) $\theta=49^{\circ}$ (subtraction)