Q. 485.0( 3 Votes )

In the given figure, AP, AQ and BC are tangents to the circle. If AB = 5 cm, AC = 6 cm and BC = 4 cm then the length of AP is


A. 15 cm

B. 10 cm

C. 9 cm

D. 7.5 cm

Answer :

Let tangent BC touch the circle at point R


As we know tangents drawn from an external point to a circle are equal.


We have


AP = AQ


[tangents from point A]


BP = BR …[1]


[tangents from point B]


CQ = CR …[2]


[tangents from point C]


Now,


AP = AQ


AB + BP = AC + CQ


5 + BR = 6 + CR [From 1 and 2]


CR = BR - 1 …[3]


Now,


BC = 4 cm


BR + CR = 4


BR + BR - 1 = 4 [Using 3]


2BR = 5 cm


BR = 2.5 cm


BP = BR = 2.5 cm [Using 2]


AP = AB + BP = 5 + 2.5 = 7.5 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