Question 1154490: please help me with this I don't know how to script drawings into this so
I made a link to my problem instead
https://photos.google.com/share/AF1QipMZTJWYXLs9hcm6hH2tSoHG7jLPehOIOh1dfqITVHXuBdmENIfIdenldc4RtJCzRA/photo/AF1QipMnijyDDPnX4lIedQArxgf626VAb0-sMybh6u_N?key=NlZoMzBfVlhkV3daci1PSk1POE5fSTdka0xBeG93
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Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
It is of no benefit to you for us to give you the answers. I will tell you what you need to know to find the answers; you can do the work.
I suspect you will be familiar with all of these; the learning task is to see how to apply them to the questions.
A. The measure of a central angle in a circle is the same as the measure of the intercepted arc.
B. The measure of an inscribed angle in a circle is half the measure of the intercepted arc.
C. A radius or diameter perpendicular to a chord bisects the chord; it also bisects the arc intercepted by the chord.
D. A radius or diameter is perpendicular to a tangent at the point of tangency.
E. If two chords intersect, the product of the lengths of the two parts of one is equal to the product of the lengths of the two parts of the other.
1. Given the measure of angle BOF, find the measure of arc BF.
Angle BOF is a central angle. Use A above.
2. Given the measure of angle BOC, find the measure of angle C.
Use D above to see that triangle BOC is a right triangle.
3. Given BE=26 and DF=24, find OX.
BE=26 means the radius is 13. Use C above to find FX; then find OX using the Pythagorean Theorem.
...OR (harder but still educational)...
Use E above with the lengths of FX, XD, and BE to find the lengths of BX and EX; then find the length of OX from that.
4. Given that the measure of arc DEF is 250 degrees, find the measure of arc BD.
Use C above, along with the fact that the sum of the measures of arcs DEF and FD is 360 degrees.
5. Given that the measure of arc BF is 80 degrees, find the measure of angle BEF.
Use B above.
6. Given that the measure of angle FOE is 140 degrees, find the measure of angle FDE.
Use A and B above.
Answer by ikleyn(52765)  (Show Source):
You can put this solution on YOUR website! .
In this site, there is a group of lessons that carry all necessary geometry facts to learn and to know to solve this problem
- A circle, its chords, tangent and secant lines - the major definitions,
- The longer is the chord the larger its central angle is,
- The chords of a circle and the radii perpendicular to the chords,
- A tangent line to a circle is perpendicular to the radius drawn to the tangent point,
- An inscribed angle in a circle,
- Two parallel secants to a circle cut off congruent arcs,
- The angle between two chords intersecting inside a circle,
- The angle between two secants intersecting outside a circle,
- The angle between a chord and a tangent line to a circle,
- Tangent segments to a circle from a point outside the circle,
- The converse 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 point outside a circle
- Quadrilateral inscribed in a circle
- Quadrilateral circumscribed about a circle
There are also lessons on solved problems for circles, their chords, secant and tangent lines are
- HOW TO bisect an arc in a circle using a compass and a ruler,
- HOW TO find the center of a circle given by two chords,
- Solved problems on a radius and a tangent line to a circle,
- Solved problems on inscribed angles,
- A property of the angles of a quadrilateral inscribed in a circle,
- An isosceles trapezoid can be inscribed in a circle,
- HOW TO construct a tangent line to a circle at a given point on the circle,
- HOW TO construct a tangent line to a circle through a given point outside the circle,
- HOW TO construct a common exterior tangent line to two circles,
- HOW TO construct a common interior tangent line to two circles,
- Solved problems on chords that intersect within a circle,
- Solved problems on secants that intersect outside a circle,
- Solved problems on a tangent and a secant lines released from a point outside a circle and
- The radius of a circle inscribed into a right angled triangle
- Solved problems on tangent lines released from a point outside a circle
Also, you have this free of charge online textbook on Geometry
GEOMETRY - YOUR ONLINE TEXTBOOK
in this site.
The referred lessons are the part of this online textbook under the topic "Properties of circles, inscribed angles, chords, secants and tangents ".
Save the link to this online textbook together with its description
Free of charge online textbook in GEOMETRY
https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson
to your archive and use it when it is needed.
In these severe quarantine days, you have happy opportunity to learn Geometry from good source and enrich your mind (!)
Enjoy (!)
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