Question

Three sides of a quadrilateral ABCD are AB=10cm. BC=7cm. CD=9cm. What can be the length of the fourth side, DA, if it can circumscribe a circle?

Answer 1

Solution:-
The sides AB, BC, CD and DA of the quadrilateral ABCD touches the circle at P, Q, R and S respectively.
We know that, the length of tangents drawn from an external point to a circle are equal.
AP = AS ...(1)
BP = BQ ...(2)
CR = CQ ...(3)
DR = DS ...(4)
Adding (1), (2, (3) and (4), we get
(AP + BP) + (CR + DR) = (AS + DS) + (BQ + CQ)
∴ AB + CD = DA + BC
= 10 cm + 9 cm = DA + 7 cm
⇒ DA + 7 cm = 19 cm
⇒ DA = 19 cm - 7 cm
⇒ DA = 12 cm 
The length of DA = 12 cm  Answer.

Answer 2

Answer:

the answer is in the above attachment pls..thank if helpfull btw ik it will not be helpfull