Question

Converse of cyclic quadrilateral theorem
Theorem : If a pair of opposite angles of a
quadrilateral is supplementary, the quadrilateral is cyclic.
Write Given,To Prove and Proof with the diagram​

Answer 1

Step-by-step explanation:

true..

.......,...........

Answer 2

Angle at Center = 2(Angle formed on Circle)

Step-by-step explanation:

(i) $\angle$ BAD = $\frac {1}{2}$ \angle BOD

(The angle subtended by an arc at the center is double the angle on the circle.)

(ii) $\angle$ BCD  =  $\frac {1}{2}$reflex $\angle$ BOD

(iii) $\angle$ BAD + $\angle$ BCD = $\frac {1}{2}$ $\angle$BOD +  $\frac {1}{2}$reflex $\angle$ BOD

(add (i) and (ii))

$\angle$BAD + $\angle$BCD  =  $\frac {1}{2}$ ($\angle$BOD + reflex $\angle$ BOD)

$\angle$BAD + $\angle$BCD  = $\frac {1}{2} \times (360)$

(Complete angle at the center is 360°)

$\angle$ BAD + $\angle$ BCD = 180°

(iv) Similarly $\angle$ABC + $\angle$ADC = 180°