Proposed Problem

See complete Problem 276 at:

gogeometry.com/problem/p276_square_circle_90_degree_arc.htm

Level: High School, SAT Prep, College geometry

## Thursday, April 2, 2009

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## Thursday, April 2, 2009

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

Online Geometry theorems, problems, solutions, and related topics.

Proposed Problem

See complete Problem 276 at:

gogeometry.com/problem/p276_square_circle_90_degree_arc.htm

Level: High School, SAT Prep, College geometry

Subscribe to:
Post Comments (Atom)

If we've two circles of radii r1 & r2 that are tangent to each other then:

ReplyDelete(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

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

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

Sumith Peiris

Moratuwa

Sri Lanka