Circumscribed circle In calculation, the encompassed circle or circumcircle of a polygon is a circle that goes through all the vertices of the polygon. The focal point of this circle is known as the circumcenter and its range is known as the circumradius. Few out of every odd polygon has an encompassed circle. A polygon…
Suppose we have two lines in a Cartesian coordinate system, given by the equations: a1x + b1y + c1 = 0a2x + b2y + c2 = 0 The angle between these two lines can be found using the formula: tan(theta) = |(m2 – m1)/(1 + m1*m2)| where m1 and m2 are the slopes of the…
To find the equation of a line passing through the point of intersection of two given lines, you can follow these steps: Note: If the two given lines are parallel, they will never intersect, and there will be no point of intersection. In this case, it is not possible to find a line passing through…
To find the distance between a point and a line in analytical geometry, you can use the formula: distance = |ax + by + c| / √(a^2 + b^2) where a, b, and c are constants that represent the coefficients of the equation of the line in the form of ax + by + c…
In analytical geometry, the angle between two lines can be found using the slopes of the lines. The slope of a line is defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. Let the equations of two lines be: L1: y…
In analytical geometry, the distance between two points in a plane is given by the distance formula: d = sqrt((x2 – x1)^2 + (y2 – y1)^2) where (x1, y1) and (x2, y2) are the coordinates of the two points and d is the distance between them. To use the formula, simply substitute the values of…
Trigonometric functions are mathematical functions that relate the angles of a right triangle to the lengths of its sides. The most commonly used trigonometric functions are sine (sin), cosine (cos), and tangent (tan). These functions can be defined in terms of the sides of a right triangle as follows: In addition to these three functions,…
Standard deviation and variance are measures of variability that provide information about how spread out a dataset is. The standard deviation is the square root of the variance, and it measures the average deviation of each data point from the mean. In general, the larger the standard deviation or variance, the more spread out the…
Mean deviation is a measure of variability that describes the average difference between the values in a dataset and their mean. It is also known as mean absolute deviation (MAD). The formula for calculating the mean deviation is: Mean Deviation = (Σ |xi – x̄|) / n where: Σ represents the sum of the absolute…
Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted by P(A|B) and read as “the probability of A given B”. The formula for conditional probability is: P(A|B) = P(A and B) / P(B) Where P(A and B) is the probability of A and B occurring…
