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)