Q. 254.0( 2 Votes )

In Fig., a ΔABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ΔABC is 84 cm2.


Answer :

Given: area of ΔABC is 84 cm2.


To find: The length of AB and AC.


Theorem Used:


The length of two tangents drawn from an external point are equal.


Explanation:



Firstly, consider that the given circle will touch the given circle will touch the sides AB and AC of the triangle at a point E and F respectively.


Let AF=x


Now in triangle ABC


C is an external point and CF and CD are the tangents drawn from it.


CF = CD=6cm


Similarly, BE = BD =8cm (tangent is drawn from external point B)


AE = AF =X


Now AB= AE + EB =x + 8


Also, BC = BD+ DC = 8+6 =14


and CA= CF+FA = 6+ x


Now we get all side of the triangle and its area can be find by using heron’s formula











Squaring both side and solving we get,
x(x+14)-7(x+14) =0
or x=-14and7
x=-14 is not possible
so x=7
hence AB=7+8=15cm
CA=6+7=13
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 Circles37 mins
Short Cut Trick to Find Area of Triangle43 mins
Quiz | 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
view all courses