In convex quadrilateral `A B C D ,A B=a ,B C=b ,C D=c ,D A=d` . This quadrilateral is such that a circle can be inscribed in it and a circle can also be circumscribed about it. Prove that `tan^2A/2=(b c)/(a d)dot`

Explanation

To prove that \( \tan^2 \frac{A}{2} = \frac{bc}{ad} \) for a convex quadrilateral \( ABCD \) with sides \( AB = a \), \( BC = b \), \( CD = c \), and \( DA = d \), and given that a circle can be inscribed and circumscribed about it, we will follow these steps:

### Step 1: Use the properties of the quadrilateral
Since the quadrilateral \( ABCD \) can have both an inscribed circle and a circumscribed circle, we can use the following properties:
1. For an inscribed circle: \( a + c = b + d \) (the sum of opposite sides is equal).
2. For a circumscribed circle: \( A + C = 180^\circ \) (the sum of opposite angles is \( 180^\circ \)).

### Step 2: Express \( \cos A \) using the Law of Cosines
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