wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In a triangle ABC, the internal bisectors of angle B and C meet at P and the external bisector of the angle B and C meet at Q.
Prove that : BPC + BQC = 2 rt. angles.

Open in App
Solution


ABC+ext.ABC=180o (Angles on a straight line)

12(ABC+ext.ABC)=90o

PBC+QBC=90o (PB bisect Interior B, QB bisects ext.B)

PBQ=90o

Similarly, PCQ=90o
Sum of angles of quadrilateral PBCQ =360o

BPC+PBQ+PCQ+BQC=360o

BPC+BQC=180o

BPQ+BQC = 2 rt. angles

204205_194234_ans_3beda39a4d714061a1dec7ebf96c965b.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Locus of the Points Equidistant from a given point
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon