Question

A quadri lateral ABCD is circumscribed
to ellipse whose diagonals passes.
through opposite foci of ellipse
AB=5 BC=6 CD=7 find AD​

Answer 1

A quadrilateral ABCD is circumscribed  to ellipse whose diagonals passes.

through opposite foci of ellipse  AB=5 BC=6 CD=7 and AD​=2√3.

Given,

AB=5

BC=6

CD=7

Let AD​ = x

Since the quadrilateral ABCD is circumscribed  to ellipse, we can divide this quadrilateral into 2 right angles triangles,

quad ABCD = tri ABC + tri ADC

Δ ABC and Δ ADC

In Δ ABC,

AC^2 = AB^2 + BC^2

AC^2 = 5^2 + 6^2

AC^2 = 25 + 36

AC^2 = 61

AC = √61

Now, consider,

In ΔADC,

AC^2 = AD^2 + DC^2

(√61 )^2 = x^2 + 7^2

61 = x^2 + 49

61 - 49 = x^2

12 = x^2

x = √12

∴ AD = √12 = 2√3