Q. 34.5( 4 Votes )

I drew a circle having PR as a diameter. I draw a tangent at tangent at the point P and a point S is taken on the tangent of the circle in such a way that PR = PS. If RS intersects the circle at the point T. Let us prove that ST = RT = PT.

Answer :

Theory.


Angle sum property of triangle is 180°


if 2 sides of triangle are equal then their corresponding angles will also be equal


Solution.



In Δ PRS


PS = PR


PSR = PRS


RPS = 90° (Radius of circle from point of contact of tangent is 90° )


PSR + PRS + RPS = 180°


2PSR = 180° - 90°


PSR = 45°


PSR = PRS = 45°


In Δ PRT


PTR = 90° (3rd point of triangle on circumference of semicircle is always 90° )


PRT = PRS = 45°


TPR + PRT + PTR = 180°


TPR = 180° - 135°


= 45°


PRT = TPR


RT = TP (isosceles triangle property)………1


In Δ PTS


RPS = TPS + TPR = 90°


TPS + 45° = 90°


TPS = 45°


PST = PSR = 45° (proved above)


PST = TPS


PT = ST (isosceles triangle property)………2


Joining 1 and 2


We get ;


PT = ST = RT


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Area Related with the Circle45 mins
Quiz | Area Related with Circles47 mins
Quiz | A Letter to God39 mins
A Letter to God45 mins
A Letter to God50 mins
Time-Management: A key to Success37 mins
How to build a strong Vocabulary?53 mins
Let's Calculate - A Guide to an Economist's Dictionary54 mins
Tricks to MemoriseFREE Class
Smart and Effective study is the Key of success45 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
RELATED QUESTIONS :