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July 28, 2023
To solve questions effectively and accurately in placement exams you need to have a stronghold on the tips, tricks and shortcuts of that chapter. This page will provide you with all possible Tips Tricks and Shortcuts of Geometry questions types which are frequently asked in the exams.
The Tips Tricks of Coordinate Geometry and Shortcuts are listed below with the sample questions.
We can solve this manually. But with the help of a tips and tricks and shortcut that is discussed in this page of PrepInsta
Scenario 1:
When Perimeter is odd
Scenario 2:
When perimeter is even
Scenario 1 – Details
Solution – In this case, total number of triangles will be the nearest integer to \frac{P^2}{48} \
Scenario 2 – Details
Solution – In this case, total number of triangles will be the nearest integer to \frac{(P+3)^2}{48} \
Question 1:
ABCD is a square. AD is tangent to circle with radius r and OE = ED. Then what is the ratio of the area of circle to the area of square?
Optionsa) \frac{Π}{3} \
b) \frac{Πr^2}{3} \
c) \frac{Πr^2}{4} \
d) \frac{2Πr}{4r} \
Explanations
OD2 = OA2+ AD2
(2r)2 = r2 + AD2
Thus PQ, which is also the side of square, is equal to r√3. The area of square becomes: 3r2Hence the ratio of the area of circle to square is:
\frac{area of circle}{area of square} \ = \frac{πr^2}{3r^2} \ = \frac{π}{3} \
Correct Option (A)
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Question 2
If in a triangle ABC, \frac{cos A}{a} \ = \frac{cos B}{b} \ = \frac{cos c}{c} \ , then what can be said about the triangle ?
OptionsA) Right angled triangleB) Isosceles triangleC) Equilateral triangleD) Nothing can be inferred
From the sine rule of triangle we know, \frac{a}{sinA} \ = \frac{b}{sinB} \ = \frac{c}{sinC} \ = k
Therefore, a = k(sin A), b = k(Sin B) and c = k(Sin C)
Hence, we can rewrite, \frac{cos A}{a} \ = \frac{cos B}{b} \ = \frac{cos C}{c} \ as \frac{cos A}{k Sin A} \ = \frac{cos A}{k Sin B} \ = \frac{cos C}{k Sin C} \
or Cot A= Cot B= Cot CA = B = C, Hence the triangle is equal.
Correct Option (C)
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