Question

Rhombus ABCD has side length ‘l’, with



cos B = -2/3



. The circle through

points A, B and D has radius 1, find ‘l’.​

Answer 1

REF.Image.

Given :

ABCD is a rhombus

AC and BD interest are O

E any point on circle

with centre O.

To field :- Sum of measure

of ∠BAE and ∠EDC

Sol

n

:- Since ABCD is a rhombus

and diagonals of rhombus bisect at 90

∘

So, ∠BOC=90

∘

and similarly ∠DOA=90

∘

Now we have a shown that angle drawn on the centre

of the circle by the same are is qoulde the ...(1)

angle drawn on any other point on the circle

So, it from the are BEC angles ∠BAC=

2

1

∠BOC.and ∠BOC=90

∘

So ∠BAC=

2

90

∘

=45

∘

from the same theorem we have that ∠BDC=90

∘

...(ii)

(drawn from same are BEC)

Now we have a theorem that angles drawn from same

are of a circle are equal

⇒ angle from are BE→ means ∠BAE=∠BDE...(iii)

(drawn from same are BE)

again similarly from are EC→∠EDC=∠EAC...(iv)

(drawn from same are EC).

from (1) ∠BAE=∠BDE

adding ∠EDC both side

∠BAE+∠EDC=∠BDE+∠EDC=∠BDC=45

∘

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