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

I is the incenter of ABC. IF P and Q be the feet of perpendicular from A to BI and CI, respectively, then APBI+AQCI=

A
cotA2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
tanA2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
sinA2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
cosA2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A cotA2
In APB,sinB2=APAB

n AQC,sinC2=AQAC

Now, In ABI, we have

BIsinA2=ABsin(πA2B2)=ABcosC2

and in ACI, we have CIsinA2=ACcosB2

So, APBI+AQCI=sinB2cosC2sinA2+sinC2cosB2sinA2

=sin(B2+C2)sinA2=cosA2sinA2=cotA2

389990_142536_ans_c821488b3eef42049fea2e9277ee48a9.png

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Transformations
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon