Krishna
0

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}