A, B and C are points on the circumference of a circle with centre O, AB and AD are tangents to the circle. Angle BAD = 70°. Work out the size of angle BCD

Step 1: Observe the given figure and note down the given information
Step 2: Calculate the unknown angles ( \angle ADO and \angle ABO) by using the hints in the question.
NOTE: According to the Perpendicular Tangent Theorem, tangent lines
are always perpendicular to a circle's radius at the point of intersection.
Tangent of the circle is always perpendicular to radius
EXAMPLE: From the figure \angle ADO = \angle ABO = 90
Step 3: Calculate the Central angle ( \angle BOD) by using the properties quadrilateral
NOTE: The sum of the angles in any convex quadrilateral is 360 degrees.
EXAMPLE: From the figure ABOD is a quadrilateral
\angle ADO + \angle ABO + \angle DAB + \angle BOD = 360
\angle BOD = 360 - (\angle ADO + \angle ABO + \angle DAB)
\angle BOD = 360 - (90 + 90 + 70)
\angle BOD = 360 - 250
\angle BOD = 110
Step 4: Calculate the inscribed angle ( \angle DCB)
NOTE: The Central Angle Theorem states that the central angle from two
chosen points A and B on the circle is always twice the inscribed angle from
those two points.
EXAMPLE: Central angle = 110
Inscribed angle ( \angle DCB) = \frac{\text{Central angle}}{2}
Inscribed angle \angle DCB = \frac{110}{2}