If a circle goes through all four corner points of a four-sided figure, that means the four vertices lie on the circle. The term for any quadrilateral with all four vertices on a circle is a cyclic quadrilateral. This is the broad description that fits any shape with that property, not just one specific type. Note that a rectangle is a special case of a cyclic quadrilateral (its four vertices do lie on a circle), but the question asks for the general description of a figure whose corners touch the circle, which is captured precisely by cyclic quadrilateral. Parallelogram and rhombus don’t automatically have all four corners on a circle unless they happen to be rectangles (or squares), so they don’t describe the given situation as reliably.

The main idea here is a proof by contradiction. You suppose that the statement you want to prove is false (its negation), and then you reason using valid axioms and logic to see what would follow. If this leads to a contradiction—something that cannot be true given the established rules—then the initial assumption must be false, so the original statement is true. This is also known as reductio ad absurdum in many contexts. Direct proofs go straight from the axioms to the conclusion without assuming the negation. Inductive proofs establish a claim for all natural numbers by proving a base case and showing that if it holds for one case, it holds for the next. Empirical proofs rely on observation and experimentation rather than formal deduction.

This is about giving every member of the population an equal chance to be selected, with the selection driven entirely by random chance and without dividing the population into subgroups. In simple random sampling, you treat all individuals as a single pool, assign each a unique identifier, and draw the sample randomly (for example, using a random number generator or a lottery). Because no subgroup structure is used, every person has exactly the same probability of being chosen, and the method avoids systematic patterns or stratification that could bias the results. In contrast, systematic sampling selects at regular intervals, which can introduce bias if there’s an underlying pattern; stratified sampling divides the population into subgroups and samples within each one; quota sampling fills predefined subgroup numbers without random selection.

In statistics, the value you record for one member of the sample is an observation (often called a data point). Each element of the sample yields one observation, and collecting all of them together forms the data set. If you’re measuring just one variable, the data set is univariate data. Data capture, by contrast, refers to the process of recording the data, not the value itself. So the single numeric value for one element is best described as an observation.