Question

Inside a quadrilateral ABCD, there is point O, which is equidistant from all the four sides. If AB=3cm, BC=5cm, CD=6cm, find AD.

Answer 1

2 cm.

Draw perpendiculars from point O to all the sides.  Join O with all vertices.

Comparing the two right angles Δ OBE and OBF,  BE = BF , by applying Pythagoras theorem in both Δs :

       OB² = BE² + R² = BF² + R²       =>  BE = BF

Similarly,  CF = CG ,   DH = DG,   AE = AH  in other triangles.

Now let  BE = x.                           then BF = x.
now   CF = 5 - x.                          then  CG =  5 -x
now   GD = 6 - (5 - x)  = x - 1       so then  DH = x - 1
Now,  AE = 3 - x,                          so then AH = 3 - x     

So finally,   AD = AH + HD = 3 - x + x - 1   = 2 cm.

that is the answer.

Answer 2

Answer:

pls refer the above attachment the correct answer will be 4 not 2 as in the earlier answer