Step-by-step explanation:
Angle CBO = 90 - 2x because the radius meets the tangent at 90°
Angle OCB = Angle CBO= 90 - 2x because base angles of an isosceles triangle are equal (OB and OC are radii - so they are equal)
Angle DCO = Angle CDO = x because base angles of an isosceles triangle are equal. (OC and OD are radii - so they are equal)
Angle BCD = Angle DCO + Angle OCB
So Angle BCD = x + (90 - 2x)
Angle BCD = 90 - x
therefore, Angle DOB = 2 × (90 - x)
Angle DOB = 180 - 2x because the angle at the centre is twice the angle at the circumference.
Angle ODA and Angle OBA are both 90° as the angle between the radius and the tangent is 90°
hence, you can work out Angle DAB because angles in a quadrilateral add up to 180°.
Angle DAB = y
y = 360 - 90 - 90 - (180 - 2x)
expand brackets
y = 360 - 90 - 90 - 180 + 2x
y = 2x (angles in a quadrilateral add up to 360°)
