Question

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal

Answer 1

$\mathfrak{The\:Answer\:is}$


Equation of the given line is
(x-2)/3=(y-3)/5=(z-4)/4...........(1)
Equation of the given plane is
2x-2y+z+5=0............................(2).
Let us find angle between normal to plane (2) and line (1).If θ is the angle then cosθ=(3*2-5*2+4*1)/√(50)√(9)=0
=> angle between normal to plane and given line is 90°.Hence line (1) is parallel to the plane (2.)


$\boxed{Hope\:This\:Helps}$

Answer 2

Let ABCD is The cyclic quardilateral

Join AC and BD.


To prove AC = BD

Proof In ΔAOD and ΔBOC,

∠OAD = ∠OBC and ∠ODA = ∠OCB


AB = BC [given]

ΔAOD = ΔBOC [by ASA ]

Adding is DOC on both sides, we get

ΔAOD+ ΔDOC ≅ ΔBOC + ΔDOC

⇒ ΔADC ≅ ΔBCD

AC = BD [by CPCT]

thanks me Later ❤️