A circle with centre P is inscribed in the ABC. Side AB, side BC and side AC touch the
circle at points L, M and N respectively. Radius of the circle is r.
Prove that: A(ABC) = 1
2
(AB + BC + AC) r.
Answers
Answer:
Repetition Statements
The other type of important programming control structure is a repetition statement. A repetition statement is used to repeat a group (block) of programming instructions. Most beginning programmers have a harder time using repetition statements than they have at using selection statements. At the same time, the use of repetition statements is at least (if not more) important than using selection statements. Therefore, it is a good idea to expect to spend more time trying to understand and use repetition statements.
Repetition statements fall into two general categories; while loops and for loops. Although it is possible to write every loop as a while loop (or every loop as a for loop), this is not a good idea. While loops should be used if the number of repetitions is not fixed. In many cases, the number of repetitions that a while loop executes depends on user input. On the other hand, for loops should be used when the number of repetitions is fixed. In many cases, the number of repetitions a for loop executes for is determined by the number of elements in an array or an array-like object (such as a list or a tuple in Python). This is why for loops are often associated with some indexed quantity like a list.
While loops
As mentioned earlier, while loops are used when a block of statements have to be repeated, but the number of repetitions is not a fixed amount. This means that a while loop might repeat two times when a program is run and repeat a different number of times the next time that same program is run. This feature makes while loops flexible. Unfortunately (as mentioned before), this flexibility comes at the expense of being more complex.
A good way to start thinking about how while loops work is to think in terms of the following algorithm:
While the task is not done
repeat these instructions
This gives a feel for why while loops don't always repeat the same number of times. It may take a different number of repeats for the task to get done. Actually, the above algorithm is lacking in some important details. The next algorithm fills in those important details.
While (condition 1 is true)
do some instruction(s)
If (condition 2 is true)
Set condition 1 to be false
What this algorithm suggests is that most while loops have two conditions that are involved. As long as condition 1 is true, the while loop repeats. But, a selection statement (based on a second condition) will cause condition 1 to become false at some point to end the loop. The important thing to take note of here is that somewhere in the while loop's block, there must be some instructions that cause condition 1 to be false. Otherwise, the while loop becomes an infinite loop (a loop that repeats forever).
To get a better feel for writing a while loop, consider the following program. You want to write a program that will be asking for the names of all the members in a club. However, we don't know how many members are actually in the club. Thus, once the while loop starts, the while loop will simply repeat until all the member's names have been entered. The following is an algorithm that could be used to solve this problem.
Step-by-step explanation:
hope this helps you
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