Q. 55.0( 1 Vote )

In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively.

If AB = x cm, BC = 7 cm, CR = 3 cm and

AS = 5 cm, find x.


Answer :

As we know, Tangents drawn from an external point are equal.


CR = CQ [tangents from point C]


CQ = 3 cm [as CR = 3 cm]


Also,


BC = BQ + CQ


7 = BQ + 3 [BC = 7 cm]


BQ = 4 cm


Now,


BP = BQ [tangents from point B]


BP = 4 cm …[1]


AP = AS [tangents from point A]


AP = 5 cm [As AC = 5 cm] ….[2]


AB = AP + BP = 5 + 4 = 9 cm [From 1 and 2]


AB = x = 9 cm


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Quiz | Imp. Qs. on CircleQuiz | Imp. Qs. on CircleQuiz | Imp. Qs. on Circle35 mins
Quiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on CirclesQuiz | Imp. Qs. on Circles37 mins
Quiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on CirclesQuiz | Testing Your Knowledge on Circles32 mins
Short Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of TriangleShort Cut Trick to Find Area of Triangle43 mins
Quiz | Areas Related to CirclesQuiz | Areas Related to CirclesQuiz | Areas Related to Circles43 mins
RD Sharma |  Area of Sector and SegmentsRD Sharma |  Area of Sector and SegmentsRD Sharma | Area of Sector and Segments25 mins
Quiz | Area Related with CirclesQuiz | Area Related with CirclesQuiz | Area Related with Circles47 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses