6. Five marks exercise problems - III

1. Two circles with centres \(O\) and \(O'\) of radii \(3 \ cm\) and \(4 \ cm\), respectively intersect at two points \(P\) and \(Q\), such that \(OP\) and \(O'P\) are tangents to the two circles. Find the length of the common chord \(PQ\).

  

  

2. In \(\Delta ABC\), with \(\angle B = 90^\circ\), \(BC = 6 \ cm\) and \(AB = 8 \ cm\), \(D\) is a point on \(AC\) such that \(AD = 2 \ cm\) and \(E\) is the midpoint of \(AB\). Join \(D\) to \(E\) and extend it to meet at \(F\). Find \(BF\).

 

Answer:

 

The value of \(BF\) \(=\)  \(cm\)

 

 

3. An artist has created a triangular stained glass window with one strip of small length left before completing the window. She needs to figure out the length of left-out portion based on the lengths of
the other sides, as shown in the figure.