# Question Bank - Geometry - Hemant Malhotra

• 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 circumcenter

C(x, y) ........ G(1, -1) ................. O (5, 3)
CG = 2GO

So 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 = -3

So 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 ?

65

153

33

32

102

33

149

102