Thursday, April 2, 2009

Problem 276: Square, 90 degree Arcs, Circle, Radius

Proposed Problem

Problem 276: Square, 90 degree Arcs, Circle, Radius.

See complete Problem 276 at:
gogeometry.com/problem/p276_square_circle_90_degree_arc.htm

Level: High School, SAT Prep, College geometry

2 comments:

  1. If we've two circles of radii r1 & r2 that are tangent to each other then:
    (common tangent)^2 = (r1+r2)^2 -(r1+r2)^2
    = 4r1r2
    In this case, the common tangent = a/2 while r1 =x and r2 =a. Thus, (a/2)^2 = 4xa or a^2/4 =4xa
    or x=a/16
    QED
    Ajit: ajitathle@gmail.com

    ReplyDelete
  2. Apply Pythagoras to Tr. ADM where.M is the centre of the circle with radius x.

    (a + x)^2 = (a-x)^2 + a^2. from which it follows that x = a/16.

    Sumith Peiris
    Moratuwa
    Sri Lanka

    ReplyDelete