Q. 18

In ΔABC, sides AB and AC are produced to D and E respectively. BO and CO are the bisectors of CBD and BCE respectively. Then, prove that


Answer :


Here BO, CO are the angle bisectors of DBC &ECB intersect each other at O.


∴∠1 = 2 and 3 = 4


Side AB and AC of ΔABC are produced to D and E respectively.


Exterior of DBC = A + C ………… (1)


And Exterior of ECB = A + B ………… (2)


Adding (1) and (2) we get


DBC + ECB = 2 A + B + C.


22 + 23 = A + 180°


2 + 3 = (1 /2)A + 90° ………… (3)


But in a ΔBOC = 2 + 3 + BOC = 180° ………… ( 4)


From eq (3) and (4) we get


(1 /2)A + 90° + BOC = 180°


BOC = 90° – (1 /2)A


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
NCERT | Angle Sum PropertyNCERT | Angle Sum PropertyNCERT | Angle Sum Property44 mins
Quiz | Lines and AnglesQuiz | Lines and AnglesQuiz | Lines and Angles40 mins
Quiz | Lines and AnglesQuiz | Lines and AnglesQuiz | Lines and Angles43 mins
Lines and AnglesLines and AnglesLines and Angles45 mins
Quiz | Lines and AnglesQuiz | Lines and AnglesQuiz | Lines and Angles45 mins
NCERT | Intersecting and Non Intersecting lines)NCERT | Intersecting and Non Intersecting lines)NCERT | Intersecting and Non Intersecting lines)41 mins
NCERT | Discussion on Lines And AnglesNCERT | Discussion on Lines And AnglesNCERT | Discussion on Lines And Angles45 mins
Quiz | Angle Sum Property of TriangleQuiz | Angle Sum Property of TriangleQuiz | Angle Sum Property of Triangle40 mins
NCERT | Lines and Angles Part - 1NCERT | Lines and Angles Part - 1NCERT | Lines and Angles Part - 142 mins
Quiz | Imp. Qs. on Lines and AnglesQuiz | Imp. Qs. on Lines and AnglesQuiz | Imp. Qs. on Lines and Angles30 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses