Angles on a tangent

A secondary school revision resource for GCSE Maths about higher level shapes and circles. Try to work out the size of angles RPQ, SPR and PSR. The angle between the tangent and chord at the point of contact is equal to the angle in the alternate segment. This is the circle property that is the most difficult to spot.

In the pythagorean theorem, c^is the hypotenuse.

Circle Theorem GCSE Maths revision section.

Explaining circle theorem including tangents , sectors, angles and proofs, with notes and videos.

This means that the measure of arc ABC (the purple portion of the circle itself) is twice the measure of angle C. Tangents , Secants, arcs and their angles. The theorems and formuala for the rules for theses intersections. Note: It can be proven that ∠ABC and central angle ∠AOC are supplementary.

Thus the angle formed by the two tangents and the degree measure of the first minor intercepted arc also add to 180º . For more information about manipulating the figure, see About the applet. Where the edge of the circle meets. As the secant line moves away from the center of the circle, the two points where it cuts the circle eventually merge into one and the line is then the tangent to the circle.

As can be seen in the figure above, the tangent line is always at right angles to the radius at . Sal finds missing angles using the property that tangents are perpendicular to the radius. Let me actually label this line. In the above diagram, the angles of the same color are equal to each other.

Geometrically this corresponds to computing the angle formed by the tangent lines and the line of centers, and then using that to rotate the equation for the line of centers to yield an equation for the tangent line. You will also understand that the length of two tangents from an external point are Equal. FREE resource, activities and worksheets. This maths video will explain this IGCSE . A printable version of this page may be downloaded here. If you need it, this theorem is set out here and all the theorems are summarised here.

Angle between tangent and radius. The second property is that the angle from .