SOLUTION: In ∆ PQR, │PQ│= 9cm, │QR│= 11cm, │RP│= 7cm and the bisector of ln ∠P meets line QR at T. Calculate │QT│ and│TR│.

Question 1210339: In ∆ PQR, │PQ│= 9cm, │QR│= 11cm, │RP│= 7cm and the bisector of ln ∠P meets line QR at T. Calculate │QT│ and│TR│.
Answer by ikleyn(52748) (Show Source): You can put this solution on YOUR website!
.
In ∆ PQR, │PQ│= 9cm, │QR│= 11cm, │RP│= 7cm and the bisector of ln ∠P meets line QR at T.
Calculate │QT│ and│TR│.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

In every triangle, every its angle bisector has this remarkable property:


    the foot of the angle bisector divides the side of the triangle 
    in the ratio equal to the ratio of the adjacent sides.


Therefore, in triangle PQR, the bisector PT of angle P
divide the side QR of 11 cm long in the ratio

     = ,    (1)

or

     = .    (2)


Together with  QT + TR = QR = 11 cm,  it gives


    QT =  =  cm = 6 cm,    (3)

    TR =  =  cm = 4 cm.   (4)


ANSWER.  QT =  =  cm = 6 cm;  TR =  =  cm = 4 cm.

Solved.

--------------------------

Try to deduce formulas (3) and (4) from formula (2) on your own.

RELATED QUESTIONS
Line segment PQ and PR are congruent sides of isosceles triangle PQR. The bisector of... (answered by richard1234)

Triangle PQR has PQ=8cm, QR= 10cm and angle PQR is 40�. Calculate the area of triangle... (answered by stanbon)

QT and PM are altitude of ∆PQR. If |QR| = 8cm, |PR| = 7cm and QT = 4cm, what is |PM| (answered by ikleyn)

PQR is a triangle, given that /PQ/=15m, /QR/=17m and /RP/=18m. Find the area of the... (answered by ikleyn,Edwin McCravy)

Which of the following uses the given set of points to prove that △MNO≅△PQR?... (answered by Boreal)

PQRS is a parallelogram, the bisector UT of line QR cuts line SR at T. If angle PSR =... (answered by greenestamps)

In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, (answered by greenestamps,math_tutor2020)

In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with... (answered by Timnewman,Edwin McCravy,greenestamps)

triangle PQR has PQ = 150 and PR = QR = 125, as shown. Three line segments are drawn... (answered by ikleyn)