Monday, May 19, 2008

Elearn Geometry Problem 54

See complete Problem 54
Tangent Circles, angle bisector, midpoint. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.


  1. No problema 53, temos que BM é bissetriz do ângulo CBE. Como ângulo CBM = ângulo DBM, temos que arcoCM = arco MD. Fica provado que M é ponto médio de CD.


    Connect FH, AE, OAB and OFG
    Drawing OM perpendicular to CD. OM will intersect arc CD at midpoint M .
    We will prove that M,E,B and G, M, H are collinear
    1. Tri. EAB and MOB are isosceles with EA//MO
    m(MOB)=m(EAB) (corresponding angles)
    so m(OMB)=m(ABE) and M, E, B are collinear

    2. Similarly with tri. MOG and HFG
    With the same logic as step 1 we will prove that G,H,M are collinear.

    So GH and BE meet at M , midpoint of arc CD

    Peter Tran

  3. Thank you for giving me a chance to comment.