In a quadrilateral $A B C D$
$A B + B C + C D + D A > 2 A C$
Say true or false.

True

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False

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Ambiguous

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Data insufficient

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Solution

The correct option is A True
$I n t h e q u a d r i l a t e r a l A B C D . C o n s i d e r △ A B C A B + B C > A C : s u m o f t w o s i d e s i s g r e a t e r t h a n t h e t h i r d s i d e - > 1 I n △ A D C A D + D C > A C : s u m o f t w o s i d e s i s g r e a t e r t h a n t h e t h i r d s i d e - > 2 A d d i n g 1 a n d 2 w e g e t A B + B C + A D + D C > 2 A C$

Suggest Corrections

Similar questions

A B C D

A B + B C + C D + D A > 2 A C

A B C D

A B + B C + C D > D A

A B C D

A B + B C + C D + D A > 2 B D

A B C D

(A B + B C + C D + D A) < 2 (A C + B D)

ABCD is a quadrilateral , Is AB +BC+CD+DA < 2(AC+BD)

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