Question

In a quadrilateral klmn kn=lm and angle knm=lmn. Prove that points k l m and n lie on circle

Answer 1

Step-by-step explanation:

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Answer 2

In a quadrilateral klmn kn=lm and angle knm=lmn.

Hence it is proved that points k l m and n lie on circle

Given:

KLMN is a quadrilateral.

KN=LM,

∠ KNM = ∠ LMN.

 To prove:

That the quadrilateral klmn is cyclic

 ⇒ All points lie on the circle.

 Proof:

KN = LM (given)

As, the opposite sides of the quadrilateral are equal.

Therefore, the quadrilateral KLMN is a Rectangle.

We know that,

 A quadrilateral is said to be cyclic quadrilateral, if and only if, when it's opposite angles form 180°

 But all angles of a rectangle are 90°

 Therefore,

∠ KNM + ∠ KLM

=   90° + 90°

 = 180°

 Therefore, quadrilateral KLMN is cyclic.

Hence it is proved that, the points  k, l, m, n lie on the circle.