1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find the Circumradius for a Triangle

  1. May 1, 2013 #1


    User Avatar
    Gold Member

    Let ABC is an acute angled triangle with orthocentre H. D, E, F are feet of perpendicular from A, B, C on opposite sides. Let R is circumradius of ΔABC.

    Given AH.BH.CH = 3 and (AH)2 + (BH)2 + (CH)2 = 7, answer the following
    [tex]\frac{\prod \cos A}{\sum \cos^{2}A}[/tex]Q2. What is the value of R?

    ANS 1. From properties of triangle, the distance of Orthocentre from a point A is given by AH = 2R.cosA. Using the values of cosines and from information in the question, I solved the first question to get the answer 3/14R.

    Now I have no clue on how to approach Q2. I can't seem to find any relation between the value of R and information given to me. BTW, from what I know, the answer mentioned is 3/2.
  2. jcsd
  3. May 1, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    What does the answer to Q1 tell you?
    Why is it important that the triangle is acute angled?
  4. May 1, 2013 #3


    User Avatar
    Gold Member

    Acute angled triangle means all the cosines are greater than zero?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted