ABC is a right triangle at C,a perpendicular CD is drawn at AB prove AC^2/BC^2=AD/BD.?

Question

Sridhar R · Accepted Answer

in triangle ACD
   angle ACD  +  angle CAD  = 90

in triangle  ACB
   angle CAB +   ABC  = 90

  angle CAB  = angle CAD    same angle


therefore   angle ACD  =  angle  ABC  --------------------------------(1)


consider the Triangles  

  ACD  and CBD

    angle ACD  =  angle  CBD  |  angle ABC = angle CBD
   angle  ADC  =   angle  CDB

 so the two triangles are similar 

so we have

   AD/CD  = AC/CB  =  DC/DB  -----------------------------------2)

   AD/DC  =  AC/BC
   DC/BD   = AC/BC   | from 2

 multiplying both
 AD/DC   *  DC/BD   =  AC/BC  *  AC/BC

    AD /BD  =  AC^2/BC^2   prooved

? · Answer

Find the distance between the points d, e, and f and if the distance is equal between all of them then they make an equilateral triangle.

ABC is a right triangle at C,a perpendicular CD is drawn at AB prove AC^2/BC^2=AD/BD.?

2 個解答