Prove that the angle bisectos of a cyclic quadrilateral forms another quadrilateral which is also cyclic.
Asked by
21st February 2013,
10:58 PM
Answered by Expert
Answer:
ABCD is a cyclic quadrilateral
?A + ?C = 180 and ?B + ?D = 180
(?A + ?C)/2 = 90 and (?B + ?D)/2 = 90
?A + ?C = 180 and ?B + ?D = 180
(?A + ?C)/2 = 90 and (?B + ?D)/2 = 90
x + z = 90 and y + w = 90
In ?AGD and ?BEC,
x + y + ?AGD = 180 and z + w + ?BEC = 180
?AGD = 180 (x+y) and ?BEC = 180 (z+w)
?AGD + ?BEC = 360 (x+y+z+w) = 360 (90+90) = 360 180 = 180
?AGD+?BEC = 180
?FGH+?HEF = 180
The sum of a pair of opposite angles of a quadrilateral EFGH is 180.
Hence EFGH is cyclic
In ?AGD and ?BEC,
x + y + ?AGD = 180 and z + w + ?BEC = 180
?AGD = 180 (x+y) and ?BEC = 180 (z+w)
?AGD + ?BEC = 360 (x+y+z+w) = 360 (90+90) = 360 180 = 180
?AGD+?BEC = 180
?FGH+?HEF = 180
The sum of a pair of opposite angles of a quadrilateral EFGH is 180.
Hence EFGH is cyclic
Answered by Expert
22nd February 2013,
4:51 PM
Rate this answer
- 1
- 2
- 3
- 4
- 5
- 6
- 7
- 8
- 9
- 10
You have rated this answer /10
Your answer has been posted successfully!
RELATED STUDY RESOURCES :
Browse free questions and answers by Chapters
- 1 Number System
- 2 Polynomials
- 3 Coordinate Geometry
- 4 Linear Equations in Two Variables
- 5 Introduction to Euclid's Geometry
- 6 Heron's Formula
- 7 Surface Areas and Volumes
- 8 Statistics
- 9 Probability
- 10 Lines and Angles
- 11 Triangles
- 12 Quadrilaterals
- 13 Areas of Parallelograms and Triangles
- 14 Circles
- 15 Geometric Constructions
Trending Tags
Latest Questions
ICSE IX Mathematics
Asked by aadrica.kanika
17th October 2018,
6:44 PM
