▁b ', ▁c ' ▁▁ ▁being ▁the ▁actual ▁per pend icular ▁distances ▁to ▁the ▁sides ▁satisfy ▁ ▁for ▁triangle ▁sides ▁a , ▁b , ▁c ▁and ▁area ▁. ▁This ▁can ▁be ▁seen ▁in ▁the ▁figure ▁at ▁the ▁top ▁of ▁this ▁article , ▁with ▁interior ▁point ▁P ▁partition ing ▁triangle ▁ABC ▁into ▁three ▁tri angles ▁P BC , ▁P CA , ▁and ▁P AB ▁with ▁respective ▁areas ▁( 1 / 2 ) aa ' ▁, ▁( 1 / 2 ) bb ' ▁, ▁and ▁( 1 / 2 ) cc ' ▁. ▁ ▁Dist ance ▁between ▁two ▁points ▁ ▁The ▁distance ▁d ▁between ▁two ▁points ▁with ▁actual - distance ▁tr il ine ars ▁a ' ▁i ▁: ▁b ' ▁i ▁: ▁c ' ▁i ▁is ▁given ▁by ▁ ▁Dist ance ▁from ▁a ▁point ▁to ▁a ▁line ▁ ▁The ▁distance ▁d ▁from ▁a ▁point ▁a ' ▁ 0 ▁: ▁b ' ▁ 0 ▁: ▁c ' ▁ 0 , ▁in ▁tr il ine ar ▁coordinates ▁of ▁actual ▁distances , ▁to ▁a ▁straight ▁line ▁l x ▁+ ▁my ▁+ ▁n z ▁= ▁ 0 ▁is ▁ ▁Qu adr atic ▁curves ▁ ▁The ▁equation ▁of ▁a ▁con ic ▁section ▁in ▁the ▁variable ▁tr il ine ar ▁point ▁x ▁: ▁y ▁: ▁z ▁is ▁ ▁It ▁has ▁no ▁linear ▁terms ▁and ▁no ▁constant ▁term . ▁ ▁The ▁equation ▁of ▁a ▁circle ▁of ▁radius ▁r ▁having ▁center ▁at ▁actual - distance ▁coordinates ▁( a ', ▁b ', ▁c ' ▁) ▁is ▁ ▁Circ um con ics ▁ ▁The ▁equation