question_answer

The diameter of a circle with centre at C is 50 cm. CP is a radial segment of the circle. AB is a chord perpendicular to CP and passes through P. CP produced intersects the circle at D. If \[DP=18\text{ }cm,\]then what is the length of AB?

A)  \[24\text{ }cm\]                      

B)  \[\text{32 }cm\]

C)  \[\text{40 }cm\]                     

D)  \[\text{48 }cm\]

Correct Answer: D

Solution :

              \[\Delta \,ACP,\] \[CP=CD-PD=25-18=7\]                 Now,  \[A{{C}^{2}}=C{{D}^{2}}+A{{P}^{2}}\]                 \[\therefore \,\,\,AP=\sqrt{A{{C}^{2}}-C{{P}^{2}}}=\sqrt{{{(25)}^{2}}-{{(7)}^{2}}}\]                 \[=\sqrt{625-49}=\sqrt{576}=24\,cm\] Similarly, \[PB=24\text{ }cm\] \[\therefore \text{ }AB=AP+PB=24+24=\]