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- ...<math>BC</math> and <math>AC</math> are perpendicular, <math>AC</math> is tangent to <math>\omega</math>. Let the line <math>AB</math> meet <math>\omega</ma == External links ==6 KB (943 words) - 09:44, 17 January 2025
- # One of the lines is [[tangent line|tangent]] to the circle while the other is a [[secant line|secant]] (middle figure) ...o a circle and intersect it at <math>A</math> and <math>B</math>. A third tangent meets the circle at <math>T</math>, and the tangents <math>\overrightarrow{5 KB (948 words) - 16:04, 21 February 2025
- ...hat <math> \overline{AD}</math> and <math> \overline{BC}</math> are common external tangents to the circles. What is the area of hexagon <math> AOBCPD</math>?13 KB (2,058 words) - 11:36, 4 July 2023
- ...h>3-4-5</math> right triangle are the centers of three mutually externally tangent circles, as shown. What is the sum of the areas of the three circles? ...e radii <math>3</math> and <math>8</math>, respectively. A common internal tangent intersects the circles at <math>C</math> and <math>D</math>, respectively.15 KB (2,223 words) - 12:43, 28 December 2020
- ...ent. A third circle is tangent to the first two and to one of their common external tangents as shown. The radius of the third circle is13 KB (1,957 words) - 11:53, 24 January 2024
- ...hat <math> \overline{AD}</math> and <math> \overline{BC}</math> are common external tangents to the circles. What is the area of hexagon <math> AOBCPD</math>? ...angle OAD</math> and <math>\angle ADP</math> are right angles due to being tangent to the circles, and the altitude creates <math>\angle OHD</math> as a right3 KB (458 words) - 15:40, 6 October 2019
- ...h>9</math>, respectively. The equation of a common external [[tangent line|tangent]] to the circles can be written in the form <math>y=mx+b</math> with <math>2 KB (295 words) - 01:24, 30 October 2024
- ...are all collinear. A chord of <math> C_3 </math> is also a common external tangent of <math> C_1 </math> and <math> C_2. </math> Given that the length of the ...f a circle that is externally tangent to <math> w_2 </math> and internally tangent to <math> w_1. </math> Given that <math> m^2=\frac pq, </math> where <math>7 KB (1,119 words) - 20:12, 28 February 2020
- ...[[collinear]]. A [[chord]] of <math> C_3 </math> is also a common external tangent of <math> C_1 </math> and <math> C_2. </math> Given that the length of the ...e{O_1O_2}</math> at a point <math>H</math>. Let the endpoints of the chord/tangent be <math>A,B</math>, and the foot of the perpendicular from <math>O_3</math4 KB (693 words) - 12:03, 28 December 2021
- ...ally tangent]] to two circles adjacent to it. All circles are [[internally tangent]] to a circle <math> C </math> with [[radius]] 30. Let <math> K </math> be ...nt circles as <math>r</math>. If we draw all of the radii to the points of external tangency, we get a [[regular polygon|regular]] [[hexagon]]. If we connect t1 KB (213 words) - 12:17, 22 July 2017
- ...The circle of radius <math>9</math> has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord.6 KB (1,000 words) - 23:25, 26 March 2024
- ...math>P</math> are such that <math>AD</math> and <math>BC</math> are common external tangents to the circles. What is the area of the [[concave]] [[hexagon]] <m ...0), B=tangent(X, O, 2, 1), A=tangent(X, O, 2, 2), C=tangent(X, P, 4, 1), D=tangent(X, P, 4, 2);3 KB (541 words) - 13:41, 4 November 2024
- ...The circle of radius <math>9</math> has a chord that is a common external tangent of the other two circles. Find the square of the length of this chord. ...to <math>\overline{PQ}</math> (so <math>A_3,A_6</math> are the points of [[tangent (geometry)|tangency]]). Then we note that <math>\overline{O_3A_3} \parallel3 KB (605 words) - 10:30, 5 May 2024
- ...math>P</math> are such that <math>AD</math> and <math>BC</math> are common external tangents to the circles. What is the area of the concave hexagon <math>AOBC14 KB (2,059 words) - 00:17, 30 January 2024
- ...pproximates a curve at a point. That is, if you zoom in very closely, the tangent line and the curve will become indistinguishable from each other at a certa ...ht)</math> intersects it in [[infinite]]ly many points (and is in fact the tangent line at each point of intersection).2 KB (332 words) - 20:54, 11 March 2024
- He also discovered the power series for the [[tangent function|arctangent]], which is ==External Links==3 KB (503 words) - 22:28, 1 November 2024
- ...ath> at <math>B</math> and <math>C</math> meet at <math>I_a</math> and the external bisectors at <math>A</math> and <math>C</math> intersect at <math>I_b</math30 KB (4,794 words) - 22:00, 8 May 2024
- Let <math>l</math> and <math>l'</math> be internal and external bisectors of the angle <math>\angle BPC, l \perp l'</math>. Let <math>\triangle ABD</math> be external for <math>\triangle ABC</math> equilateral triangle <math>\implies F = CD \59 KB (10,203 words) - 03:47, 30 August 2023
- ...o the extension of [[leg]] <math>CB</math>, and the circles are externally tangent to each other. The length of the radius either circle can be expressed as ...s. As <math>\overline{AF}</math> and <math>\overline{AD}</math> are both [[tangent]]s to the circle, we see that <math>\overline{O_1A}</math> is an [[angle bi11 KB (1,853 words) - 19:10, 21 July 2024
- An '''excircle''' is a [[circle]] [[Tangent line|tangent]] to the extensions of two sides of a [[triangle]] and the third side. ...that there is one, if any, circle such that three given distinct lines are tangent to it.5 KB (843 words) - 02:02, 1 July 2020