Q. 523.8( 10 Votes )

In Fig. 5, PQ is

Answer :

PT is perpendicular to OP (Tangents are always perpendicular to the center)

PQ is perpendicular to OT (The line joining the Point of contact of common tangents with the center is perpendicular to the common tangent)


Let length of PT be x and length of RT be y


Since PR is perpendicular to OT so by using Pythagoras theorem we calculate OR


Length of PR = 4 cm (Half of PQ)


OR2 = 52 - 42


OR = 3 cm


Using Pythagoras theorem:


PR2 + RT2 = PT2


16 + y2 = x2 … Equation(i)


PT2 + OP2 = OT2


x2 + 52 = (3 + y)2


x2 + 52 = 9 + y2 + 6y


Putting the value of x2 from equation (i) we get


16 + y2 + 52 = 9 + y2 + 6y


6y = 32


y =


Putting the above value in Equation (i) we get




Answer: The length of PT =

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Bonus Questions on CirclesBonus Questions on CirclesBonus Questions on Circles40 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