IIT JEE , AIEEE Forum - Mathematics , Algebra

Mr.IITIAN007

Let ABC be a triangle.Take n points on the side AB (different from A and B ) and connect all of them by straight lines to the vertex C. Similarly , take n points on the side AC and connect them to B.In how many regions is the triangle ABC partitioned by these lines ?

Further , take n points on the side BC also join them with A . Assume that three straight lines meet at a point other than A,B and C.In how many regions is the triangle partitioned now ?

pink_ele

for first part

no of reigions=no of quads formed by intersecting lines+2(n-1)i.e small triangles at ends +1(gap in bet. these two reigons of small triangles)+2(n-1)(extra quads formd by lines and resp. side+2(two other small triangles+1(big upper quad)

=nC2XnC2+4(n-1)4+4

=(nC2)+4n

plzzzzzzzz make second part clear

how can 3diff lines mett at two pts

draw fig you will get yaar!!!

rate me if rite!!!!!!!!!!!!!!!!!!

nick

when u take n points on AB and join it with C it gives (n+1) partition,

similarly for the other when n points on AC join B (n+1)

hence total no. of partition are (n+1)(n+1)....

pirate1_from_jee

4 the frst prt,

Is it (n+1⁾²

Mr.IITIAN007

Hey what the hail is that ?

pirate1_from_jee

Yar s it okkkkkkkkk.
2nd prt 2 morrow.Is t crrct????

CRUSADE

GOOD JOB pirate1-from-jee YOU ASKED ME" WHO ARE YOU?"I am CRUSADE and my name is PRIYAM DAS(ISI2007)

devesh_l2k007

when u partition in into n the triangle gets partitioned into n+1
for 1st case ans is (N+1)square
case 2 N+1 cube

krishna.gopal

Only one question at a time. Answer to first part is (n+1)^2

spideyunlimited

1) (n+1)^2

2) (n+2).2n

Ask & Discuss Questions with Community & Experts