Posts tagged 'tangent-to-circle'
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.118 perpendicular at extremity of a diameter is tangent
The line drawn at right angles to the diameter of a circle from its extremity falls outside the circle, no other line can be interposed between it and the arc, and the angle of the semicircle is greater than any acute rectilineal angle.
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.141 construct a circle segment on a chord admitting a given angle
On a given segment, construct a segment of a circle admitting an angle equal to a given rectilineal angle.
G.142 cut off a circle segment admitting a given angle
From a given circle, cut off a segment admitting an angle equal to a given rectilineal angle.
G.145 converse of the tangent-secant theorem
If from a point outside a circle a secant and a segment to the circle are drawn such that the rectangle on the whole secant and its external part equals the square on the segment, the segment is tangent to the circle.
G.149 inscribe a triangle in a circle equiangular with a triangle
Inscribe in a given circle a triangle equiangular with a given triangle.
G.151 circumscribe a triangle about a circle equiangular with a triangle
Circumscribe about a given circle a triangle equiangular with a given triangle.
G.159 circumscribe a square about a circle
Circumscribe a square about a given circle.
G.162 construct a golden isosceles triangle
Construct an isosceles triangle having each of the angles at the base double the remaining angle.
G.164 circumscribe a regular pentagon about a circle
Circumscribe an equilateral and equiangular pentagon about a given circle.
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.