Question

three sides of a quadrilateral ABCD are a b equals to 10 cm BC equals to 7 cm CD is equals to 9 cm what can be the length of fourth side a 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.