Question Bank  Geometry  Hemant Malhotra

2set can be triangle formation

The insect can go from A to B either in exactly 3 steps or in exactly 5 steps.
No: of ways to go from A to B in exactly 3 steps = (3C1) * (2C1) = 6 ways.because at vertex A it has to choose 1 edge out of 3 which it will do in 3C1 ways. and at each vertex 1 or 3 or 5 it has to choose 1 edge out of 2 edges which it will do in 2C1 ways.
No: of ways to go from A to B in exactly 5 steps = No: of ways to go from A to B in exactly 5 steps when no edge is traversed more than once + No: of ways to go from A to B in exactly 5 steps when one of the edge is traversed more than once.
No: of ways to go from A to B in exactly 5 steps when no edge is traversed more than once = 6 ways.
now lets find out the number of ways when insect goes from A  1  A, that is it has completed 2 steps and is back to A from which it has to reach B in remaining 3 steps which it can do in 6 ways.
so when edge A1 is repeated = 6 ways. when edge A3 is repeated = 6 ways, when edge A5 is repeated = 6 ways.
hence (6 + 6 + 6) = 18 ways
now say the insect go from vertex A to any of the three vertex . lets say it goes from A to 1 here when edge 12 is repeated then insect has 2 ways and when 16 is repeated insect has 2 ways. so total 4 ways, hence 3C1*4 = 12 ways.one more case is there when insect travels from A1232B third side is repeated here also 6 ways will be there.
hence total number of ways = 6 + 6 + 18 + 12 + 6 = 48 ways

Let A be the point at which the goat is tied.
Now the radius of the circle is 21
So Total area of the circle will be pie r^2 = pie * 21 *21
But it covered 3/4 th of the circle + Some extra part
So it will be 3/4 (pie * 21^2) + Red part + Yellow part
= 3/4( pie * 21^2) + 1/4(pie * 14^2) + 1/4(pie * 7^2)
= 1232
OA = A[credits : @hemant_malhotra]

@hemant_malhotra 218............

Funda 1 : In any triangle, the orthocenter, circumcenter and centroid are collinear (Euler line)
Funda 2 : On the Euler line the centroid G is between the circumcenter O and the orthocenter H and is twice as far from the orthocenter as it is from the circumcenterC(x, y) ........ G(1, 1) ................. O (5, 3)
CG = 2GOSo point G divides CO in the ratio 1 : 2. Time for the next funda!
Funda 3 : Section Formula
If point P lies on segment AB and satisfies AP : PB = m : n then P = ( (mx2 + nx1)/(m + n), (my2 + ny1)/(m + n) )
Here,
1 = (5 + 2x)/3 => x = 1
1 = (3 + 2y)/3 => y = 3So C is (1, 3)
Now try this.
If the orthocentre of a triangle is (3,5) and the circumcentre is (6,2) then what is the centroid?

@hemant_malhotra wouldn't 57 be the maximum common median ?

@hemant_malhotra Ans 7.4?
r= sqrt(6.75^2+3.05^2)= 7.41 approx.

@hemant_malhotra Ans 26 ?

@hemant_malhotra Sir, 49? Two triangles can be formed, one with ABC 24 area and another with ACD 25 area.

@hemant_malhotra By similarity d.5/4

@hemant_malhotra b. 18rt2

@hemant_malhotra a+p = 2l+2b+lb = (l+2)(b+2)4 = 100/102/104/106/108 only 102+4 = 106= 53*2 not possible . so 102 ?

@hemant_malhotra Is 43 the maximum perimeter possible ?

@hemant_malhotra using mass point geometry i got answe as 1/2 (144)=72 ?

@hemant_malhotra 50 intersection points ??

@hemant_malhotra 7.4 is the answer !!

@hemant_malhotra said in Question Bank  Geometry  Hemant Malhotra:
Q8) PQ and RS are perpendicular chords of a circle intersecting at T. RT= 2.5, TS=11, PT= 3. Find the radius of the circle (approximately).
a) 4.5
b) 12.1
c) 7.4
d) 15.67.41

@hemant_malhotra said in Question Bank  Geometry  Hemant Malhotra:
Q21) A right circular cylindrical vessel having height 20 cm and inner diameter 10 cm is filled with water upto 15 cm of it's height as measured from the base. Find the angle by which the cylinder must be tilted so that the water in the cylinder is just about to fall out?
45° ??

@hemant_malhotra said in Question Bank  Geometry  Hemant Malhotra:
Q22) The sides of a triangle of area 6 are in AP. If the sides have integer lengths, what is the length of the longest side?
5