Question

If non - parallel sides of trapezium are equal prove that it is cyclic .

Answer 1

In ΔAED and ΔBFC,
AD = BC     (Given)
DE = CF    (Distance between parallel sides is same)
∠AED = ∠BFC = 90°
ΔAED ≅ ΔBFC  (RHS Congruence criterion)
Hence ∠DAE = ∠CBF  (CPCT)  … (1)
Since AB||CD, AD is transversal
∠DAE + ∠ADC = 180°  (Sum of adjacent interior angles is supplementary)
⇒ ∠CBF + ∠ADC = 180°  [from (1)]
Since sum of opposite angles is supplementary in trapezium ABCD.
Thus ABCD is a cyclic trapezium 

Answer 2

Hi there!

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For solutions, Refer to the attached picture.
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Let's see some related topics :

⚫ Circle : The collection of all the points, which are at a fixed distance from a fixed point in a plane, is called a circle.

⚫ Radius : A line joining the centre to the Circumference of the circle, is called radius of a circle.

⚫ Secant : A line intersecting a circle at any two points, is called secant.

⚫ Diameter : A chord passing through the point of the circle, is called diameter. It is the longest chord.

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