Theorem : Opposite Angles of a Cyclic Quadrilateral are Supplementary.

Solution :

Given: ABCD is a cyclic quadrilateral.
R.T.P.(Require To Prove)

1. &#x2220BAD + &#x2220BCD = 180
     2. &#x2220ABC + &#x2220ADC = 180

Construction : Join OB and OD
Proof:

1. &#x2220 BOD = 2 ∠BAD || Angle at the centre of a circle is twice the angle at the circumference.
2.  Reflex &#x2220 BOD + &#x2220 BOD = 2 (&#x2220BAD + &#x2220BCD) || Same as stated above.
  or   2 (&#x2220BAD + &#x2220BCD) = 360 || By statement 2.
or   (&#x2220BAD + &#x2220BCD) = 180
3. Similarly by joining OA and OC it can be proved that
  &#x2220ABC + &#x2220ADC = 180
4.   &#x2220BAD + &#x2220BCD = 180
&      &#x2220ABC + &#x2220ADC = 180   Proved

READ :  Theorem | the angle subtended by an arc of a circle | at the centre is double the angle subtended by it at | any point on the remaining part of the circle

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