Posts tagged 'tangent'
G.103 tangent circles
Circles are said to:term:**touch one another** <circles-touching> which, meeting one another, do not cut one another.
G.104 touching circles have distinct centers
Two circles that touch one another do not have the same center.
G.109 line of centers of internally touching circles
If two circles touch one another internally, the line joining their centers passes through the point of contact.
G.110 line of centers of externally touching circles
If two circles touch one another externally, the segment joining their centers passes through the point of contact.
G.111 line tangent to a circle
A:term:segment <G.4> is said to:term:**touch a circle** <tangent-to-circle> which, meeting the:term:circle <G.10> and being produced, does not cut the circle.
G.112 two circles touch at most at one point
A circle does not touch another circle at more than one point, whether internally or externally.
G.119 draw a tangent to a circle from a point
From a given point, construct a line tangent to a given circle.
G.120 radius to point of contact is perpendicular to tangent
If a line touches a circle, the segment joined from the center to the point of contact is perpendicular to the tangent.
G.121 perpendicular to tangent at contact passes through center
If a line touches a circle, the line drawn at right angles to the tangent from the point of contact passes through the center of the circle.
G.140 alternate segment theorem
If a line touches a circle and a chord is drawn from the point of contact, the angles which the chord makes with the tangent equal the angles in the alternate segments of the circle.
G.144 tangent-secant theorem
If from a point outside a circle a secant and a tangent are drawn, the rectangle contained by the whole secant and its external segment equals the square on the tangent.
G.150 polygon circumscribed about a circle
A:term:polygon <G.12> is said to be:term:**circumscribed about a circle** <circumscribed-about-circle>, when each side of the circumscribed:term:figure <G.9> touches the arc of the:term:circle <G.10>.
G.153 circle inscribed in a polygon
Similarly a:term:circle <G.10> is said to be:term:**inscribed in a figure** <circle-inscribed-in-figure> when the arc of the circle touches each side of the:term:figure <G.9> in which it is inscribed.
G.574 circles center inscribe
Given two circles about the same center, to inscribe in the greater circle an equilateral polygon with an even number of sides which does not touch the lesser circle.
G.577 spheres center inscribe
Given two spheres about the same center, to inscribe in the greater sphere a polyhedral solid which does not touch the lesser sphere at its surface.