(Geometry: points in triangle?) Suppose a right triangle is placed in a plane as shown below. The right-angle point is placed at (0, 0), and the other two points are placed at (200, 0) and (0, 100). Write a
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- (Display Magic Numbers) Display the first N magic numbers, where N is a positive number that the user provides as input. Here, a magic number is a number whose sum of its digits eventually leads to 1. For example, 1234 is a magic number because 1+2+3+4 = 10 and 1 +0 = 1, while 1235 is not (1 +2+ 3 +5 = 11 and 1 +1 = 2). Write a program that prints out the first N magic numbers, seven on each line. Here is the sample output: Enter a positive integer number: 30 1 10 19 28 37 46 55 64 73 82 91 100 109 118 127 136 145 154 163 172 181 190 199 208 217 226 235 244 253 262 You are required to use the following function prototype: bool isMagic(int value); // Returns true if value is a magic number The outline of this function will be as follows: Step 1: Calculate the sum of digits of value Step 2: Repeat Step 1 until we get a single digit Step 3: If the resulting sum is equal to 1 then it is a magic number, otherwise notarrow_forward(Find future dates) Write a program that prompts the user to enter an integer for today’s day of the week (Sunday is 0, Monday is 1, …, and Saturday is 6). Also prompt the user to enter the number of days after today for a future day and display the future day of the week.arrow_forward(Geometry: point in a circle?) Write a program that prompts the user to enter apoint (x, y) and checks whether the point is within the circle centered at (0, 0) withradius 10. For example, (4, 5) is inside the circle and (9, 9) is outside the circle, asshown in Figure 3.7a.(Hint: A point is in the circle if its distance to (0, 0) is less than or equal to 10.The formula for computing the distance is 2(x2 - x1)2 + (y2 - y1)2. Test yourprogram to cover all cases.) Two sample runs are shown below: Enter a point with two coordinates: 4 5Point (4.0, 5.0) is in the circleEnter a point with two coordinates: 9 9Point (9.0, 9.0) is not in the circlearrow_forward
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