In the diagram, eleven circles of four different sizes are drawn. Each circle labelled W has radius 1, each circle labelled X has radius 2, the circle labelled Y has radius 4, and the circle labelled Z has radius r. Each of the circles labelled W or X is tangent to three other circles. The circle labelled Y is tangent to all ten of the other circles. The circle labelled Z is tangent to three other circles. Determine positive integers s and t for which r = s/t
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
In the diagram, eleven
sizes are drawn. Each circle labelled W has
radius 1, each circle labelled X has radius 2,
the circle labelled Y has radius 4, and the
circle labelled Z has radius r. Each of
the circles labelled W or X is tangent to
three other circles. The circle labelled Y is
tangent to all ten of the other circles. The
circle labelled Z is tangent to three other
circles. Determine positive integers s and t
for which r = s/t
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