High School

We appreciate your visit to In triangle ABC the angle bisectors are AD BE and CF which intersect at the incenter I If tex angle ACB angle ABC tex then. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

In triangle ABC, the angle bisectors are AD, BE, and CF, which intersect at the incenter I. If [tex]\angle ACB < \angle ABC[/tex], then:

a) [tex]\angle ACD < \angle BEC[/tex]
b) [tex]\angle ADB < \angle CEI[/tex]
c) [tex]\angle AIC > \angle CIB[/tex]
d) [tex]\angle AIB < \angle BCF[/tex]

Answer :

If ∠ACB < ∠ABC, then option c) ∠AIC > ∠CIB

The correct answer is c.

The correct option is:

c) ∠AIC > ∠CIB

Explanation:

In a triangle, the angle bisector divides the opposite side into segments that are proportional to the adjacent sides. Since[tex]\( \angle ACB < \angle ABC \)[/tex] , side AC is shorter than side AB. Therefore, in triangle ABC, side AC, which is opposite to ∠ACB, is shorter than side AB, which is opposite to ∠ABC.

Thus, in triangle ABC, AI, which is the angle bisector of ∠ACB, bisects side AC, and CI, which is the angle bisector of ∠ABC, bisects side AB. Since side AC is shorter, the angle bisector AI is longer than CI. Therefore, [tex]( \angle AIC > \angle CIB \).[/tex]

The correct answer is c.

Thanks for taking the time to read In triangle ABC the angle bisectors are AD BE and CF which intersect at the incenter I If tex angle ACB angle ABC tex then. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada