Question
Statement-I : Circumradius and inradius of a triangle can not be 12 and 8 respectively.
Statement-II : Circumradius ≥ 2 (inradius)
- Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
- Statement-I is true, Statement-II is true ; Statement-II is NOT a correct explanation for statement-I.
- Statement-I is true, Statement-II is false.
- Statement-I is false, Statement-II is true.
Hint:
use the property
r <= R/2 to check whether statement 1 is correct. r = inradius and R = circumradius.
The correct answer is: Statement-I is false, Statement-II is true.
Statement-I is true, Statement-II is true ; Statement-II is correct explanation for Statement-I.
The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed
Lets assume the inradius to be r and circumradius to be R
We know that r /R = 4sin(A/2)sin(B/2)sin(C/2), where A,B,C are the angles of the triangle.
We know that sin(A/2)sin(B/2)sin(C/2) lies between 0 and 1/8
Therefore, r/R lies between 4x0 and 4 x 1/8
Or
r <= R/2
therefore, statement 2 is correct.
Now, inradius = 8 and circumradius = 12
12>= 2 x 8
12>= 16, which is false. Hence statement 1 is also true and statement 2 is the correct explanation of statement 1
The circumradius of a cyclic polygon is a radius of the circle inside which the polygon can be inscribed
inradius is the radius of the circle inscribed inside a polygon.
Related Questions to study
Statement-I : For n 
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Statement-II : G.M. > H.M. and (AM) (HM) = (GM)2
for real and positive numbers, we can use the property AM>=GM
the statement 2 doesn't have any connection with statement 1
Statement-I : For n N, 2n > 1 + n
Statement-II : G.M. > H.M. and (AM) (HM) = (GM)2
for real and positive numbers, we can use the property AM>=GM
the statement 2 doesn't have any connection with statement 1
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the mathematical reasoning can be proved by observing the term of the sequences
Statement-I : 1, 2, 4, 8, ......... is a G.P., 4, 8, 16, 32 is a G.P. and 1 + 4, 2 + 8, 4 + 16, 8 + 32, ....... is also a G.P.
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the mathematical reasoning can be proved by observing the term of the sequences
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for real and positive numbers, we can use the property AM>=GM
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for real and positive numbers, we can use the property AM>=GM
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If a homogenous catalytic reaction follows three alternative paths and then which of the following indicates the relative ease with which the reaction moves?
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Find out the rate law and order of reaction -
During the transformation of 
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During the transformation of the number of emitted is
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an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements. the variable n is generalized using an AP as well.
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A particle begins at the origin and moves successively in the following manner as shown, 1 unit to the right, 
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The ratio in the x direction is ¼ . The ratio in the y direction is -1/4
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the Am- Gm relation is a handy tool for solving sequence related problems. it is applicable to any sequence of numbers.
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the Am- Gm relation is a handy tool for solving sequence related problems. it is applicable to any sequence of numbers.
Let 
and 
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an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements
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an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements
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Nature of graph of a quadratic equation is given by its discriminant.
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Given, a,b,c>0
If a, b and c are three consecutive positive terms of a G.P. then the graph of y = ax2 + bx + c is
Nature of graph of a quadratic equation is given by its discriminant.
Here, a = a, b= ar, c = ar2 , where r is the common ratio of the GP
Given, a,b,c>0
If ln (a + c) , ln (c – a), ln (a – 2b + c) are in A.P., then :
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An = A1+(n-1)x d
A2= A1 + d
A3 = A1 + 2d
A3 = A2+d
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an A.P is a sequence of mathematical terms which have a common difference with their adjacent elements
An = A1+(n-1)x d
A2= A1 + d
A3 = A1 + 2d
A3 = A2+d
A3-A2=A2-A1
