18 Apr

When it comes to Govt. job exams, it is a known fact that many candidates who wish to become Bank PO or Clerk also appear in SSC CGL exam. However, the syllabus of Banking and SSC exams happens to be somewhat different. Geometry is one significant area which gets added in the quantitative aptitude section of SSC exams.

Hence, the experts from Top Bank PO Coaching Institute in Delhi suggest that candidates preparing for banking must also focus on Geometry, if they wish to appear in SSC exams. If you are also one such candidate, then the geometry tricks explained below will be of great benefit to you.

Inradius (r)
Inradius
As you can see in the figure above, Inradius is the radius of the circle which is inscribed inside the triangle.
image 1

Circumradius (R)
Circumradius
Circumradius is defined as the radius of that circle which circumscribes (surrounds) the triangle. As shown in the above figure, the circle with centre O passes through the three vertices of the triangle ABC.
image 2

 

 

 

NOTE: The ratio of circumradius to inradius in an equilateral triangle is 2:1 or (R = 2r). However, in case of other triangles this ratio is not fixed.

Question 1: Find the inradius of the triangle with sides 5, 12 & 13 cm.

a.12          b. 11.5           c. 2            d. 12.5

Solution: (C)

As sides 5, 12 & 13 form a Pythagoras triplet, which means 52+122= 132, this is a right angled triangle. Perpendicular sides will be 5 & 12, whereas 13 will be the hypotenuse because hypotenuse is the longest side in a right angled triangle.
image 6

Question 2: Find the circumradius of the triangle with sides 9, 40 & 41 cm.

a. 2          b.  4             c. 20.5          d. none of these

Solution: (C)

As sides 9, 40 & 41 form a Pythagoras triplet, which means 92+402 = 412, this is a right angled triangle. 41, which is the longest side, will be the hypotenuse.
image 3

 

 

Question 3: What is the ratio of circumference of circumcircle & circumference of incircle of an equilateral triangle?

a. 2:1       b. 1:2        c. 1:1                  d. 2:3

Solution: (A)

We know that the ratio of circumradius & inradius of an equilateral triangle is 2:1. The ratio of circumference of circumcircle & circumference of incircle will be = 2∏R/2∏r =(R/r) = 2:1

Question 4: The ratio of the areas of the circumcircle and the incircle of an equilateral triangle is

a. 2:1       b. 4:1             c. 8:1              d. 3:2

Solution: (B)

The ratio of circumradius (R) & inradius (r) in an equilateral triangle is 2:1, so R/ r = 2:1.

Ratio of area of circumcircle & that of incircle = ∏R2/∏r2 =(R/r)2 = (2:1)2  = 4:1

Question 5: The circumradius of an equilateral triangle is 14 cm. The area of the incircle of the triangle will be (Take ∏ = 22/7)

a. 154 cm2       b. 308 cm2        c. 77 cm2       d. None of these

Solution: (A)

The ratio of circumradius (R) & inradius (r) in an equilateral triangle is 2:1, so R/ r = 2:1. Here R = 14 cm. So r = R/2 = 14/2 = 7 cm. Area of incircle = ∏r2 = 22/7 X 72 = 154 cm2

Question 6: If the inradius of an equilateral triangle is 7 cm, then the circumference of the circumcircle of the triangle will be (Take ∏ = 22/7)

a. 77 cm          b. 154 cm          c. 44 cm         d. 88 cm

Solution: (D)

The ratio of circumradius (R) & inradius (r) in an equilateral triangle is 2:1, so R/ r = 2:1. Here r = 7 cm so R = 2r = 2×7 = 14 cm. The circumference of the circumcircle = 2∏R = 2 X 22/7 X 14 = 88 cm.

Question 7: What is the circumradius of an equilateral triangle of side 6 cm? 

a. 2√ 2                 b. 3√ 2                     c. 2√ 3                d. 4√2

Solution: (C)
image 4

Question 8: What is the ratio of inradius to the circumradius of a right angled triangle?    

a. 1:2               b. 1: √ 2                  c. 2:5      d. can’t be determined

Solution: (D)

The ratio of inradius to the circumradius is fixed (1:2) for an equilateral triangle. But for other triangles, this ratio is not fixed. So, the answer cannot be determined.

Question 9: The area of the incircle of an equilateral triangle of side 42 cm is

a. 231 cm2         b. 462 cm2         c. 22√ 3 cm2       d.924 cm2

Solution: (B)
image 5

 

 

 

 

The above mentioned tricks for finding the radii (inradius & circumradius) and related values in case of triangles need to be practiced and memorized. The study material offered by the centre for Best Bank Exams Coaching in Delhi has ample number of questions which cover the entire range of geometry seen in the exams.

Summary

This article on Geometry has tips & tricks which are highly useful for Govt. job exam preparation. For further clarification and guidance on how you can crack Banking and SSC exams, pls. feel free to write at vidyagurudelhi@gmail.com.

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