Question

What is the ratio of area of outermost square to that of the shaded region, if each of the marked points are the midpoints of the line segments they are touching

pls it's urgent​

Answer 1

Answer:

Handa Ka Funda

Blog

Home » Blog » Circles (Concepts, properties and CAT questions)

Circles (Concepts, properties and CAT questions)

Monday, July 20th, 2020

Circles Concepts, properties and CAT questions

Concepts of a circle are very important for CAT examinations. There are lots of properties to understand and some formulas to remember. Several direct and sometimes indirect questions are asked from concepts of a circle in CAT exams. Also, some of the geometry questions cannot be solved without having a proper understanding of CAT concepts. Let’s take a look at some of the concepts and CAT questions related to circles.

1. Arc:

An arc is just a part of a circle. An arc can be measured in degrees.

In the above diagram, the part of the circle from B to C forms an arc. Also, arc BC is equal to the angle BOC that is 45°.

1.1 Important Terms of Arcs:

(i) Measure of an Arc

1) The measure of a semi-circle is 1800.

2) The measure of a minor arc is the measure of its central angle. In the figure, BC is the minor arc with the measure 450

3) The measure of a major arc is 3600-(measure of corresponding minor arc)

m (arc BAC)=3600-m(Arc BDC) = 3600 – 450 = 3150

2. Tangent

A tangent is a line that touches a circle at only one point. A tangent is perpendicular to the radius at the point of contact.

In the above diagram, the line containing the points B and C is a tangent to the circle. It touches the circle at point B and is perpendicular to the radius OB. BC is perpendicular to OB.

3. Chord

A chord is also a line segment with both endpoints on the circle, but it may not pass through the center of the circle.

4. Secant

It is a line which intersects the circle in two distinct points. See the below figure for a definition of chord and segment

Circumference and Area of the circle

Circumference:

The circumference of a circle is the distance around a circle.

The formula for the circumference of a circle is C = πd (π =3.142)

Or C = 2πr, where C is the circumference, d is the diameter and r is the radius.

Area

The area of a circle is the region enclosed by the circle.

It is given by the formula: A = πr2 where A is the area and r is the radius.

Types of circles:

Concentric Circles: Circles lying in the same plane with a common center are called concentric circles

Tangent Circles: Circles lying in the same plane and having only one point in common are called tangent circles

One and only one circle passes through three given non-collinear points. An infinite number of circles pass through two given points.

Step-by-step explanation:

Have a good day

Answer 2

Your question is incomplete without the diagram of a square with marked points of midpoint of segment they are touching

Refer the attachment for the diagram

Solution

Assume the side of the bigger square as 4b

AD = 2√2 b

AE = 2 b

Area of outer square

$16 {b}^{2}$

Area of inner square

$8 {b}^{2}$

Area of triangle i.e AEF

$\frac{1}{2} {(2 {b}^{2} )}^{2} = 2 {b}^{2}$

Area of the shaded portion

$= 8 {b}^{2} - 2 {b}^{2} = 6 {b}^{2}$

$\frac{area \: of \: outrermost \: square}{area \: of \: the \: shaded \: portion \: in \: the \: diagram}$

$\frac{16 {b}^{2} }{6 {b}^{2} } \\ \frac{8}{3}$

Hence the ratio is 8:3