#### Question

In quadrilateral ABCD; angles D = 90°, BC = 38 cm and DC = 25 cm. A circle is inscribed in this quadrilateral which touches AB at point Q such that QB = 27 cm, Find the radius of the circle.

#### Solution

BQ and BR are the tangents from B to the circle.

Therefore, BR =BQ = 27 cm.

Also RC = (38 −; 27) = 11cm

Since CR and CS are the tangents from C to the circle

Therefore, CS = CR = 11 cm

So, DS = (25 − 11) = 14 cm

Now DS and DP are the tangents to the circle

Therefore, DS = DP

Now, `∠`PDS = 90° (given)

and OP ⊥ AD, OS ⊥ DC

therefore, radius = DS = 14 cm

Is there an error in this question or solution?

Solution In Quadrilateral Abcd; Angles D = 90°, Bc = 38 Cm and Dc = 25 Cm. a Circle is Inscribed in this Quadrilateral Which Touches Ab at Point Q Such that Qb = 27 Cm, Find the Radius of the Circle. Concept: Tangent Properties - If a Line Touches a Circle and from the Point of Contact, a Chord is Drawn, the Angles Between the Tangent and the Chord Are Respectively Equal to the Angles in the Corresponding Alternate Segments.