question_answer

In a right-angled triangle \[ABC,\,\,\angle BCA=90{}^\circ \]. CD is perpendicular from C to AB. By using the concept of area or areas of triangles, which one of the following relationships holds good?

A) \[\frac{1}{C{{D}^{2}}}=\frac{1}{B{{C}^{2}}}-\frac{1}{C{{A}^{2}}}\]

B) \[\frac{1}{C{{D}^{2}}}=\frac{1}{A{{B}^{2}}}+\frac{1}{C{{A}^{2}}}\]

C) \[\frac{1}{C{{D}^{2}}}=\frac{1}{A{{B}^{2}}}-\frac{1}{C{{A}^{2}}}\]

D) \[\frac{1}{C{{D}^{2}}}=\frac{1}{B{{C}^{2}}}+\frac{1}{C{{A}^{2}}}\]