# Tips Tricks And Shortcuts For Geometry

## Geometry Tips and Tricks and Shortcuts

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.

### From a given perimeter how many triangles with integral sides are possible?

We can solve this manually. But with the help of a tips and tricks and shortcut that is discussed in this page of PrepInsta

• We can solve this question within seconds. Generally there are two cases for these type of questions.

Scenario 1:

When Perimeter is odd

Scenario 2:

When perimeter is even

Scenario 1 – Details

• How many triangles with integral sides are possible for perimeter P where P is even

Solution – In this case, total number of triangles will be the nearest integer to $\frac{P^2}{48} \$

Scenario 2 – Details

• How many triangles with integral sides are possible for perimeter P where P is odd

Solution – In this case, total number of triangles will be the nearest integer to $\frac{(P+3)^2}{48} \$

### Tips and Tricks on Geometry

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?

Options
a)
$\frac{Π}{3} \$

b) $\frac{Πr^2}{3} \$

c) $\frac{Πr^2}{4} \$

d) $\frac{2Πr}{4r} \$

Explanations

Thus PQ, which is also the side of square, is equal to r√3. The area of square becomes:  3r2
Hence 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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### Geometry Shortcuts Tips and Tricks and Shortcuts

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 ?

Options
A)
Right angled triangle
B)
Isosceles triangle
C) Equilateral triangle
D) Nothing can be inferred

Explanations

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 C
A = B = C, Hence the triangle is equal.

Correct Option (C)

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