Angles subtended on a circle

Useful

Inscribed angle Theorem : The angle inscribed by the two points lying on the circle, at the centre of the circle is twice the angle inscribed at any point on the circle by the same points:

Angles subtended by the same segment on the circle will be equal. So here angles a and b will be equal:

Equal Chords subtend equal angles at the centre 

The angle subtended by a diameter on the circumference is a right angle

Question 1

A triangle is drawn on a clock face connecting 1, 6 and 11. What are the angles of the triangle?

Question 2

A, B, C and D are points on a circle such that ABC is a equilateral triangle and AD is a diameter of the circle. If the radius of the circle is 2 cm, what is the area of the quadrilateral ABDC?

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Angles subtended on a circle

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