This presentation explains how to construct tangents to circles and the construction of incircles and circumcircles. It defines a tangent as a line that touches a circle at only one point, a chord as a line connecting two points on the circle, and a secant as a line intersecting the circle at two points. It provides steps for constructing tangents when circles intersect, touch internally or externally, or are concentric. It also gives the process for constructing a circumcircle around a triangle and the incircle inside a triangle.

2. Tangents of the circle Presented by Deepak Kumar

6. Formation of tangent A B Secant C D P Tangent Circle Chord

8. A B C D E F G H P Q We construct four tangents AB , CD , EF & GH When two circles do not touch

10. When two circles intersect each other A B C D 1 st Tangent 2 nd Tangent O O ! . . We can construct two tangents AB , CD

11. A B O O’ When two circles touches internally We can construct only one tangents APB P

12. When two concurrent circles O O’ We can not construct any common tangent

13. P P is a point out side the circle you can construct two tangents passing through P O Q R Tangent PQ = Tangent PR

14. A B C o Constructing Circumcircle Steps of Construction Construct a Δ ABC Bisect the side AB Bisect the side BC The two lines meet at O From O Join B Taking OB as radius draw a circumcircle.

15. A B C Constructing of incircle Steps of construction Construct a Δ ABC The two lines meet at O Taking OP as radius Draw a circumcircle O P Bisect the ABC Bisect the BAC Taking O draw OP AB