Question

In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively. If the area of APQR = 189 cm² then the length of side PQ is ______.

Options

• 17.5 cm

• 20 cm

• 22.5 cm

• 25 cm

Answer 1

In the given figure, a triangle PQR is drawn to circumscribe a circle of radius 6 cm such that the segments QT and TR into which QR is divided by the point of contact T, are of lengths 12 cm and 9 cm respectively. If the area of APQR = 189 cm² then the length of side PQ is 22.5 cm.

Explanation:

`ar(ΔPQR) = 1/2 xx ("perimeter of"  ΔPQR) xx r`

⇒ `189 = 1/2 xx {(x + 12) + (12 + 9) + (9 + x)} xx 6`

⇒ x = 10.5

∴ PQ = (x + 12) cm

= (10.5 + 12) cm

= 22.5 cm