Question

In the figure, a circle is inscribed in a quadrilateral ABCD in which Angle B equal to 90°, AD = 23 cm AB =29 cm and DS = 5 cm. Find the radius of the circle,

Answer 1

so the value of r is 11

Answer 2

Answer:

Radius of the circle is 11 cm.

Step-by-step explanation:

In the figure. AB, BC, CD and DA are the tangents drawn to the circle at Q, P, S and R respectively.

∴DS=DR (tangents drawn from a external point D to the circle).

but DS = 5 cm(given)

∴ DR = 5 cm

In the fig. AD = 23 cm, (given)

∴ AR = AD - DR = 23 - 5 = 18 cm

but AR = AQ

(tangents drawn from an external point A to the circle)

∴ AQ = 18 cm

If AQ = 18 cm then (given AB = 29 cm)

BQ = AB - AQ = 29 - 18 = 11 cm

In quadrilateral BQOP,

BQ = BP (tangents drawn from an external point B)

OQ = OP (radii of the same circle)

∠QBP=∠QOP=90 °

(given)∠OQB=∠OPB=90 °(angle between the radius and tangent at the point of contact.)

∴ BQOP is a square.

∴ Radius of the circle, OQ = 11 cm