Question

Prove all the theorems of circle??​

Answer 1

Hi mate,

here's your answer

The angle subtended at the centre of a circle is double the size of the angle subtended at the edge from the same two points,

Angles which are in the same segment are equal, i.e. angles subtended (made) by the same arc at the circumference are equal,

The angles which are within a semicircle add up to 90°,

Opposite angles in a cyclic quadrilateral add up to 180°,

Alternate Segment Theorem, i.e. that the angle between a tangent and its chord is equal to the angle in the 'alternate segment'.

hope this helps you

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Answer 2

Answer:

Draw two radii as shown. Since an angle subtended at the circumference by an arc is half that subtended at the centre, the angles round the centre are 2a and 2b. Angles round a point add up to 360° so 2a + 2b = 360°. Therefore a + b = 180°, so the theorem is proven.