TANGENTS AND SECANTS OF A CIRCLE || GRADE 10 MATHEMATICS Q2

Introduction to Tangents00:00:10

A tangent line is a line that intersects a circle at exactly one point, known as the point of tangency. This section explains the definition and illustrates it with an example where line CD is tangent to a circle at point B. A postulate states that through any given point on a circle, only one tangent line can be drawn.

Theorems on Tangent Lines00:02:07

Three theorems regarding tangent lines are discussed: 1) A tangent line is perpendicular to the radius drawn to the point of tangency. 2) If a line is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. 3) If two segments from the same exterior point are tangent to a circle, then the two segments are congruent.

Common Tangents00:03:40

A common tangent is a line tangent to two circles in the same plane. There are two types: common internal tangents, which intersect the segment joining the centers of the two circles, and common external tangents, which do not.

Introduction to Secants00:04:47

A secant is a line that intersects a circle at exactly two points. This differentiates it from a tangent line, which only intersects at one point. A chord is a segment of a secant line.

Angles Formed by Two Secants Intersecting Outside the Circle00:05:58

If two secants intersect in the exterior of a circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs. An example is provided where angle CAE is calculated using the difference of arc CE and arc BD.

Angles Formed by a Secant and a Tangent Intersecting Outside the Circle00:08:04

If a secant and a tangent intersect in the exterior of a circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs. An example demonstrates calculating angle APD using arc AD and arc AB.

Angles Formed by Two Tangents Intersecting Outside the Circle0:10:36

If two tangents intersect in the exterior of a circle, the measure of the angle formed is half the positive difference of the measures of the intercepted arcs. The calculation of angle PMR is shown using arc RPQ and arc RPR.

Angles Formed by Two Secants Intersecting Inside the Circle0:13:01

If two secants intersect in the interior of a circle, the measure of the angle formed is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Examples illustrate how to find angle 1 and angle 2 using intercepted arcs.

Angles Formed by a Secant and a Tangent Intersecting at the Point of Tangency0:16:24

If a secant and a tangent intersect at the point of tangency, the measure of each angle formed is half the measure of its intercepted arc. The video provides examples for calculating angle NJk and angle MGK based on their respective intercepted arcs.