AC and DB are chords that intersect at point H.
2 answers:
Answer:
16 units
Step-by-step explanation:
see the attached figure to better understand the problem
Applying the Intersecting Chords Theorem
we have that
substitute the given values
Simplify
Find out the length of segment DB
<em>Note</em> In this problem it was not necessary to determine the value of x to calculate the DB segment.
Anyway, the calculation was done for didactic purposes.
The length of line segment DB is 16 units
<h3>Explanation: </h3>The Intersecting Chords Theorem or chord theorem states that when two chords are intersecting within a circle, the product of their respective segments is equal. This also a statement in elementary geometry that describes a relation of the four line segments created by two intersecting chords in a circle. It states that the products of the lengths of the line segments on each chord are equal.
AC and DB are chords that intersect at point H as shown in the figure below.
The intersection definition is, if the intersection happened of two sets A and B it is denoted by A ∩ B. It is the set that contains all elements of A that also belong to B, and nothing else. An intersection is a single point where two lines meet or cross each other.
Then we should find the length of the segment DB . The line segment is a part of a line with two distinct end points.
Therefore the length of line segment DB is equal to units
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I hope this helped ^^
Answer:
117
Step-by-step explanation:
First think of the square that was removed. All 4 sides are equal but you don't know the length so lets gives them the variable X.
So to find the area of the rectangle, insert those variables into the area equation for a rectangle.
(RV + (X) ) (PT +(X)) = rectangle area
Now you are given what the area is if you remove the square. So subtract the the square's area from the equation above and set it equal to the size they told you.
(RV + (X)) (PT + (X)) - [(X)(X)] = 92
rectangle - square = remaining area
Now plug in the numbers you know and solve for X.
(8 + X) (4 + X) - ((X)(X)) = 92
Use FOIL to multiply the first part of the equation (first, outer, inner, last)
32 + 8x + 4x + -
= 92
32 + 12x = 92
12x = 60
x = 5
So now you know the size of the square. Each side is 5m. So add 5m onto the top of the rectangle and onto the side. The top is 13m and the side is 9m. The area of the rectangle is the length times the height to 13 x 9 which is 117