new syllabus maths 3 , pg -250 , Q.4
In the diagram , AP, BQ and CR are the angle bisectors of A , B and C respectively. Given that A =50 , B =70 and C=60 , find P,Q and R.
what do you mean by A=50? A is an angle of ABC.
Same for P P is a point. What do you mean by "find P"?
If you want lengths of sides given the lengths of bisectors, then review the angle bisector theorem.
To find the values of P, Q, and R in the given diagram, where AP, BQ, and CR are the angle bisectors of angles A, B, and C respectively, we can apply the angle bisector theorem.
The angle bisector theorem states that in a triangle, the angle bisector of an angle divides the opposite side into segments that are proportional to the lengths of the adjacent sides.
In this case, we are given the measures of angles A, B, and C. Angle A is 50 degrees, angle B is 70 degrees, and angle C is 60 degrees.
To find P, we let BP = x and PC = y.
Since AP is the angle bisector of angle A, we know that AB/AP = BC/PC.
Since angle A = 50 degrees, we have AB/AP = BC/PC = 70/x.
To solve for x, we can use the equation AB/AP = BC/PC and substitute the given values:
70/x = 70/y
x = y (since the lengths are in the same proportion)
To find Q, we let AQ = m and QC = n.
Since BQ is the angle bisector of angle B, we know that BA/BQ = BC/QC.
Since angle B = 70 degrees, we have BA/BQ = BC/QC = 50/n.
To solve for n, we can use the equation BA/BQ = BC/QC and substitute the given values:
50/n = 50/x
n = x (since the lengths are in the same proportion)
To find R, we let CR = p and AR = q.
Since CR is the angle bisector of angle C, we know that CA/CR = AB/BR.
Since angle C = 60 degrees, we have CA/CR = AB/BR = 50/q.
To solve for q, we can use the equation CA/CR = AB/BR and substitute the given values:
50/q = 70/y
q = 70y/50 (since the lengths are in the same proportion)
Therefore, the values of P, Q, and R are given by:
P = BP = x
Q = BQ = n
R = CR = p = 70y/50
To find the specific values of P, Q, and R, we need more information. Please provide the necessary information, such as the lengths of the sides of the triangle or any additional angles.