Corresponding & Alternate angles,Nine point circle

Nine point circle (নব বিন্দু বৃত্ত) :

The circle that passes through nine significant points of a triangle, the midpoints of the three edges, the feet of the three altitudes, and the points halfway between the orthocentre and each of the three verticals.
অর্থাৎ, কোন ত্রিভুজের বাহুগুলোর মধ্যবিন্দু তিনটি, শীর্ষ হতে বিপরীত বাহুর উপর অঙ্কিত লম্বগুলোর পাদবিন্দু তিনটি এবং শীর্ষ ও লম্ব বিন্দুর সংযোজক রেখাগুলোর মধ্যবিন্দু তিনটি এই নয়টি বিশেষ বিন্দু দিয়ে যে বৃত্ত অতিক্রম করে তাকে নব বিন্দু বৃত্ত বলে।

 Corresponding Angeles : When two parallel lines are intersected by another lines called transversal the pair of angels on the same side of the transversal which is situated either above or below of the transversal are known as corresponding angels.

     

 Alternate Angeles : When two parallel lines are intersected by another line called transversal the pair of angels on the opposite side of the transversal which is situated inside or outside of the parallel lines are known as alternate  angles.

Meaning of the Mathematical term factorial : In general n! ( enn factorial ) means the product of all the whole numbers from 1 to n ; that is, n! .


5! = 5×4×3×2×1

5! = 5×4!               



n! = n×(n-1)!


Proof of zero factorial equal one :



4! = 4×3!
3! = 3×2!
2! = 2×1!
1! = 1×0!

From the last relation we found,
1!/1 = 0!
1 = 0!