Question

find it if u can... it will prove your real talent

Answer 1

$<I>The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.</I>$

$\bold{To\: Prove :}$ a+b = 2(c+d)
$\bold{Given:}$AD and BD are chords
$\bold{Proof:}$

In ∆OAD,using exterior angle theoram
a = c + c
a = 2c___________(1.)

In ∆OBD,using exterior angke theoram
b = d + d
b = 2d___________(2.)

Adding eq.(1) & (2)

a + b = 2c + 2d

a + b = 2 ( c + d )

$~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\bold{ Hence\:Proved}$