7. Five marks exercise problems - IV

1. Show that the angle bisectors of a triangle are concurrent.

 

2. Show that in a triangle, the medians are concurrent.

 

3. In a garden containing several trees, three particular trees \(P\), \(Q\), \(R\) are located in the following way, \(BP = 2 \ m\), \(CQ = 3 \ m\), \(RA = 10 \ m\), \(PC = 6 \ m\), \(QA = 5 \ m\), \(RB = 2 \ m\), where \(A\), \(B\), \(C\) are points such that \(P\) lies on \(BC\), \(Q\) lies on \(AC\), and \(R\) lies on \(AB\). Check whether the trees \(P\), \(Q\), \(R\) lie on a same straight line.