A community for students.
Here's the question you clicked on:
 0 viewing
Aadarsh
 3 years ago
From a point "P", 2 tangents, PA and PB are drawn to a circle with centre "O". If OP is equal to diameter of circle, prove that triangle PAB is an equilateral triangle.
Aadarsh
 3 years ago
From a point "P", 2 tangents, PA and PB are drawn to a circle with centre "O". If OP is equal to diameter of circle, prove that triangle PAB is an equilateral triangle.

This Question is Closed

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0Please explain with diagram.

nenadmatematika
 3 years ago
Best ResponseYou've already chosen the best response.0go angela go :D

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0Angela sister, ur figure is somewhat correct. But, we should first join OA and OB separately. Then, join AB as a separate linesegment for the triangle PAB.

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0I don't think it will help in getting the solution.

siddhantsharan
 3 years ago
Best ResponseYou've already chosen the best response.0Okay I got it but my mouse is not working properly.. If somebody could redraw a good figure labelled??

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0Wait. I am drawing the figure.

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0The only thing I have to prove is : Prove that AQ = OQ = AO = r, where "r" is the radius. If u can prove AQ = radius, I can do the rest.

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0Anyone der? Please reply soon.

Sandeez
 3 years ago
Best ResponseYou've already chosen the best response.0so you need a theorem proof?

Sandeez
 3 years ago
Best ResponseYou've already chosen the best response.0do you know any of the angles?

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0No angle. But I know that angle OAP = 90 degrees. See, in triangle, OAQ, OA = OQ = radius So, it is an isosceles triangle. Now, if we prove that AQ = radius, then it becomes an equilateral triangle.

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0AQ will be equal to radius, that's what our teacher told. She said, line segment from A on hypotenuse OP at its midpoint will be equal to the radius. But, what's the justification? What reason should I write?

Mani_Jha
 3 years ago
Best ResponseYou've already chosen the best response.1Take the point of intersection of AB and OP as I. Can you prove that OI=IQ=r/2, Aadarsh?

Mani_Jha
 3 years ago
Best ResponseYou've already chosen the best response.1Take OI=x. IP is this, (2rx). Using pythagoras' theorem, find AI from triangle AIP(AP=r*sqrt3) and then from triangle AOI. Equate those two. You will get x=r/2. After that, prove the congruency of AOI and AQI. You will get AQ=r. Do I need to show you the steps?

Mani_Jha
 3 years ago
Best ResponseYou've already chosen the best response.1Hey pls tell me if you got it

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0Can u show the steps plzzzzzzzzzzzzz?

kunal
 3 years ago
Best ResponseYou've already chosen the best response.2its easy boss................... see..... we have PO=2OA => in triangle OAP, sin(angle APO) = OA/OP => sin(angel APO) = OA/2OA = 1/2 = sin 30 => angle APO = 30 also, angle APO= angle OPB, => angle APB = 60 also AP =PB => angle ABP = angle BAP by angle sum property, all angles are 60 then its a eqvilateral triangel

Mani_Jha
 3 years ago
Best ResponseYou've already chosen the best response.1Will you accept that AP=r*sqrt3? \[AI ^{2}=PA ^{2}PI ^{2}\] =\[3r ^{2}(2rx)^{2}\] \[AI ^{2}=AO ^{2}OI ^{2}\] =\[r^{2}x ^{2}\] \[3r ^{2}(2rx)^{2}=r ^{2}x ^{2}\] Now solve this, u get x=r/2.

Aadarsh
 3 years ago
Best ResponseYou've already chosen the best response.0Thanks Kunal and Mani bhaiiiiiiii. Short and sweet proof. Cheers Kunal!!!!!!!!!
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.