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Sagot :
The characteristics of the given points are observed during the
geometric construction processes.
Responses:
Step 1: The point O is the center because it is equidistant from the three points
Step 2: PQ = PR = QR, therefore, ΔPQR is an equilateral triangle
b) The ratio of a leg to the hypotenuse side of ΔACF is 0.5, therefore, ΔACF is a 30°– 60°–90° triangle
c) The points of intersection of the diameter and a perpendicular bisector with the circumference of the circle are the vertices an inscribed square of the circle
Which process of geometric construction determines the characteristics of the given points?
Step 1: How to know that the point O is the center of the circle is as follows;
The perpendicular bisectors constructed are the locus of points
equidistant from the both points D and E and also the perpendicular
bisector gives the locus of points equidistant from points E and F
Therefore;
OE = OE, by reflexive property
OE is also equal to OF and OD by definition of the point O being on both
perpendicular bisectors.
Given that OE = OF = OD, we have that the point O is the center of a
circle with radius, OE = OF = OD passing through the points E, F, and D
Therefore;
- The point O is the center because it is equidistant from the three points
Step 2: Given that the center of the circles are the points P and Q, we have;
PQ = The radial length of the two circles
Similarly
PR and QR are radial lengths of circle P and Q respectively
Therefore;
PQ = PR = QR
Which gives;
- The lengths of the sides of ΔPQR are equal and ΔPQR is an equilateral triangle
b) FC is the diameter of circle M
Therefore;
∠ACF is 90° and ΔACF is a right triangle
The ratio of the a leg to the hypotenuse side of a 30°– 60°–90° triangle is 0.5
Length of FA = FM = MC
[tex]\dfrac{FA}{FC} = \dfrac{FA}{FM + FC} = \dfrac{FA}{FA + FA} = \dfrac{FA}{2 \times FA} = \dfrac{1}{2} = \mathbf{0.5}[/tex]
- Given that the ratio of a leg to the hypotenuse side of ΔACF is 0.5, ΔACF is a 30°– 60°–90° triangle
c) The steps that can be used to locate the vertices of a square inscribed
in a circle are;
- Draw a diameter of the circle (passing through the center)
- Construct the perpendicular bisector of the diameter, and extend it to intersect with the circle at the possible two points
- The points of intersection of the diameter and the perpendicular bisector with the circumference of the circle are the location of the vertices an inscribed square of the circle
Learn more about geometric construction here:
https://brainly.com/question/13160630
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