Question 61092: In triangle ABC , AB=AC. If there is a point P strictly between A and B such that AP=PC=CB, then angle A = ?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! In triangle ABC , AB=AC.
HENCE
ANGLE B = ANGLE C = X SAY
If there is a point P strictly between A and B such that AP=PC=CB,
IN TRIANGLE PCB , PC=CB....HENCE
ANGLE B = X = ANGLE BPC......................1
IN TRIANGLE PAC , AP=PC....HENCE
ANGLE A = Y SAY = ANGLE PCA
ANGLE C = X = ANGLE BCP + ANGLE PCA = ANGLE BCP + Y
ANGLE BCP = X-Y
ANGLE BPC = EXTERNAL ANGLE AT P FOR TRIANGLE APC
= SUM OF OPPOSITE INTERIOR ANGLES = ANGLE A + ANLE PCA = Y+Y = 2Y........2
FROM EQN.1 AND EQN.2.....X=2Y
SUM OF 3 ANGLES IN TRINGLE PBC =180 = ANGLE PBC + ANGLE BCP + ANGLE BPC
= X + X-Y+2Y =180
2X+Y=180
2*2Y+Y=180
5Y=180
Y=36
HENCE ANGLE A =36
then angle A = ? = 36
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