Two Tangents From a Point
Part of the Circles section of Coddy's Geometry journey. Lesson 50 of 62.
From a point outside a circle you can draw exactly two tangents. Their lengths, from the point to the two points of contact, are always equal. The rule is Tangents from a point.
Why? Draw OP. The triangles OTP and OUP both have a right angle, at T and at U. They share the hypotenuse OP, and their legs OT and OU are radii, so equal. Pythagoras then makes the third sides equal too: PT = PU. Here both are 7.
Challenge
PT and PU are tangents from P to circle O. Find PU, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Circles
1Parts of a Circle
Center and RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors7Angles in a Semicircle
Thales' TheoremThe Right Angle InsideIs That Enough?Semicircle With LettersRecap: Semicircles10Tangents
What a Tangent IsTangent and RadiusTangent LengthsTwo Tangents From a PointTangents With LettersRecap: Tangents2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles