CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

If in a triangle ABC, the line joining the circumcentre O and the incentre I is parallel to BC, then


A

r=RcosA

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B

r=RsinA

No worries! We‘ve got your back. Try BYJU‘S free classes today!
C

R=rcosA

No worries! We‘ve got your back. Try BYJU‘S free classes today!
D

R=rsinA

No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A

r=RcosA


Explanation for the correct option.

Find the correct relation.

The given condition that the line joining the circumcentre O and the incentre I is parallel to BC can be shown in the figure as:

As OI is parallel to BC, so O and I are equidistant from BC and thus OL=IM=r(OL⊥BC,IM⊥BC)

Now, as O is the circumcenter so ∠BOC=2A and also

∠BOL=12∠BOC=12×2A=A

Again as OB is the orthoradius, so OB=R.

Now, in â–³OBL,

cosA=OLOB⇒cosA=rR⇒RcosA=r

Hence, the correct option is A.


flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Areas of Similar Triangles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon