How to Draw a Quadrilateral in a Circle
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LetABCD be a quadrilateral circumscribed about a circle (Figure 1), |AB| = |AE| + |Exist|, From the other side, in accordance with the lesson Tangent segments to a circle from a point outside the circle nether the topicCircles and their properties of the section Geometry |AB| + |CD| = |AE| + |BE| + |CG| + |DG| = |AH| + |BF| + |CF| + |AB| + |DH| = (|AH| + |DH|) + (|BF| + |CF|) = |AD| + |BC|. Thus |AB| + |CD| = |AD| + |BC|. It is what has to be proved. The solution is completed. Solution Letx be the measure of the fourth side of our quadrilateral. Since the quadrilateral is circumscribed about a circumvolve, the sums of the measures of its contrary sides are 5 + 4 = six + x. From this equation,x = v + 4 - 6 = iii cm. Answer. The fourth side of the quadrilateral is of 3 cm long. Solution Since the trapezoid is circumscribed nigh a circle, the sums of the measures of its reverse sides are equal in accord with theProblem i to a higher place. Thus the sum Solution If a quadrilateral is circumscribed about a circle, so the sums of its contrary sides are equal. In our case the sums of the opposite sides are of 5 + seven = 12 cm If you want to navigate among my other lessons on Polygons in this site, then apply this list of links: If you desire to navigate among my lessons on circles, their chords, secant and tangent lines, then employ these links To navigate over all topics/lessons of the Online Geometry Textbook use this file/link GEOMETRY - YOUR ONLINE TEXTBOOK. Quadrilateral circumscribed about a circle
In this lesson y'all will larn that a quadrilateral confining about a circle has a specila belongings - the sums of the measures of its reverse sides are equal.
The theoretical base for solving these problems is the lesson Tangent segments to a circle from a indicate outside the circle nether the topicCircles and their properties
of the sectionGeometry in this site. Problem 1
If a quadrilateral is circumscribed about a circle, then the sums of its opposite sides are equal.
Solution
and permitEastward,F,Grand andH be the tangent points of the segmentsAB,
BC,CD andAd respectively (the sides of the quadrilateral)
and the circle. We accept
|BC| = |BF| + |CF|,
|CD| = |CG| + |DG|,
|Advert| = |AH| + |DH|.
Effigy 1. To the Problem ane
|AE| = |AH|, |BE| = |BF|, |CF| = |CG| and |AH| = |DH|
in this site. Therefore, Example 1
Find the measure of the quaternary side of a quadrilateral circumscribed nearly a circle, if 3 other sides have the measures of 5 cm, half dozen cm and iv cm listed consecutively.
equal in accordance with theProblem 1 above. Thus you can write the equation Instance two
A trapezoid is circumscribed nigh a circle. Detect the measure of the mid-segment of a trapezoid, if its lateral sides are of 5 cm and seven cm long.
of the measures of its bases is equal to the sum of the measures of its lateral sides, i.e. 5 + seven = 12 cm.
The mid-segment of a trapezoid has the measure out half the sum of the measures of its bases (see the lesson Trapezoids and their mid-lines under the topicPolygons
of the departmentGeometry in this site. So, the mid-segment of our trapezoid has the measure of = 6 cm.
Answer. The mid-segment of the trapezoid is of 6 cm long. Example 3
The sides of a quadrilateral are of v cm, 6 cm, seven sm and 8 cm long listed consecutively. Prove that this quadrilateral is non circumscribed about a circle.
and 6 + 8 = 14 cm. Since the sums are not equal, the quadrilateral is not circumscribed about a circle.
- Sum of interior angles of a polygon,
- Quadrilateral inscribed in a circle
- Regular polygons,
- The side length of a regular polygon via the radius of the circumscribed circle,
- The side length of a regular polygon via the radius of the inscribed circle,
- Miscellaneous issues on polygons and
- Backdrop OF POLYGONS
under the topicPolygons of the sectionGeometry, and
- Solved problems on interior angles of a polygon and
- Solved bug on the side length of a regular polygon
under the topicGeometry of the sectionWord issues.
- A circle, its chords, tangent and secant lines - the major definitions,
- The longer is the chord the larger its cardinal angle is,
- The chords of a circle and the radii perpendicular to the chords,
- A tangent line to a circumvolve is perpendicular to the radius drawn to the tangent point,
- An inscribed angle in a circle,
- Ii parallel secants to a circumvolve cut off congruent arcs,
- The angle betwixt ii chords intersecting inside a circle,
- The angle betwixt two secants intersecting exterior a circle,
- The angle betwixt a chord and a tangent line to a circle,
- Tangent segments to a circle from a indicate outside the circle,
- The antipodal theorem on inscribed angles,
- The parts of chords that intersect inside a circle,
- Metric relations for secants intersecting outside a circle and
- Metric relations for a tangent and a secant lines released from a indicate outside a circle
- Quadrilateral inscribed in a circle
- PROPERTIES OF CIRCLES, THEIR CHORDS, SECANTS AND TANGENTS
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