In ΔABC, the bisector of ∠ B meets AC at D. A line PQ || AC meets AB, BC, and BD at P, Q and R respectively. Show that PR x BQ = QR x BP.

Question

Philoid · Accepted Answer

Given: ∠PBR = ∠QBR & PQ ∥ AC.

In ∆BQP,

BR bisects ∠B such that ∠PBR = ∠QBR.

Since angle-bisector theorem says that, if two angles are bisected in a triangle then it equates their relative lengths to the relative lengths of the other two sides of the triangles.

So by applying angle-bisector theorem, we get

⇒ QR × BP = PR × BQ

Hence, proved.

In ΔABC, the bisector of ∠B meets AC at D. A line PQ || AC meets AB, BC, and BD at P, Q and R respectively.Show that PR x BQ = QR x BP.

In ΔABC, the bisector of ∠B meets AC at D. A line PQ || AC meets AB, BC, and BD at P, Q and R respectively.
Show that PR x BQ = QR x BP.