Hmm...III

Geometry Level 4

In $\triangle ABC$ , $\angle B = 2 \angle C$ and $D$ is a point on $BC$ such that $AD$ bisects $\angle BAC$ and $AB =CD$ .

Find $\angle BAC$ .

Submit answer in degrees.

The answer is 72.

2 solutions

Mehul Arora
Oct 25, 2014

In Triangle ABC

Given that AB = CD. Also CD=DB.

Therefore CB/2=AB. CB=2AB

By Opposite angle theorem that states that the angles opposite to equal sides are equal, and since CB=2AC,

Angle BAC=2 Angle BCA

Also Given That, Angle B= 2 angle C, Let Angle C=x

Hence, Angle B= Angle = 2x

By ASP of a triangle, x+2x+2x= 180 degrees

5x= 180 Degrees x=36 degrees

Answer = Angle A=2x=72 Degees

Very Wrong Solution.

Kushagra Sahni - 5 years, 4 months ago

RD. Sharma Class 9 XD.. Anyway this is a good geometry question when u compare it with NCERT syllabus...

Hrishik Mukherjee - 6 years ago

Why CD = DB ?

Farhan Metalestein - 5 years, 4 months ago

Teleanu Florin
Feb 14, 2016

Notations: angle B=2Y, angle C=Y, angleA=2x. Therefore, 2X+3Y=180 (1) In triangle ABC, we have that AB/sinY=AC/sin2Y and in triangle ABD, CD/sinX=Ac/sin(2Y+X). Using AB=CD we will get that sinY/sin2Y=sinX/sin(2Y+X) and by using (1) and some trigonometry we have 1/2*cos(Y)=cos(3Y/2)/cos(Y/2) which cand be solve expandind cos(3x) and find the solution A of the resulting polinomial. Then cos(y/2)=A and it must give that 2x=72

Hmm...III

Submit answer in degrees.

The answer is 72.

2 solutions

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