Styczna do okręgu - Matematyka Szkoła Podstawowa i Gimnazjum

In this video, I explain what a tangent to a circle is, how to recognize it, and how to construct it. I discuss the three possible positions of a line relative to a circle: intersecting, non-intersecting, and tangent at a single point. I explain the definition of a tangent as a line that has exactly one point in common with the circle, called the point of tangency, and I present the perpendicular relationship between the tangent and the radius drawn to that point. I teach how to construct a tangent to a circle at a given point using the perpendicular bisector of a segment, and I show how to apply this property in geometry problems, including calculating angles in triangles built from a tangent and a radius. Contents: 1. Three possible positions of a line relative to a circle 2. Definition of a tangent to a circle 3. Point of tangency 4. Perpendicularity of the tangent and the radius 5. Using tangents in triangle problems 6. Introduction to constructing a tangent 7. Step 1: drawing a ray 8. Step 2: finding the symmetric point with respect to the center 9. Step 3: constructing the perpendicular bisector of the segment 10. Step 4: drawing the tangent 11. Completing the tangent construction You can find more in the playlist: [   • GEOMETRIA NA PŁASZCZYŹNIE  ](   • GEOMETRIA NA PŁASZCZYŹNIE  ) EASY ACCESS to all my math lessons is available through my website: [www.matmagwiazdy.pl](http://www.matmagwiazdy.pl) On this channel, you will find a complete course – 100% of the lessons – in Mathematics for Primary School, High School, and Technical School. Good luck :) Tomasz D. Gwiazda 00:00 Three possible positions of a line relative to a circle 00:42 Definition of a tangent to a circle 01:39 Point of tangency 02:07 Perpendicularity of the tangent and the radius 02:45 Using tangents in triangle problems 03:36 Introduction to constructing a tangent 03:49 Step 1: drawing a ray 04:12 Step 2: finding the symmetric point with respect to the center 05:41 Step 3: constructing the perpendicular bisector 09:09 Step 4: drawing the tangent 09:34 Completing the tangent construction