6.3. In the diagram, chords DE, EF and DF are drawn in the circle with centre O. KFC is a tangent to the circle at F. Prove the theorem which states that \(\angle DFK = \beta\).
Added by Jesse J.
Close
Step 1
Since KFC is a tangent to the circle at point F, we know that angle FKC is a right angle (90 degrees). This is because a tangent line is always perpendicular to the radius of the circle at the point of tangency. Show more…
Show all steps
Your feedback will help us improve your experience
Jessica Horn and 100 other Geometry educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Craig W.
In the diagram below the two circles have radius equal to 2 and centers D and G, DH is tangent to C(G,2) at F and EF = 1. Calculate each of the following: AF, DF, AD, DC, BC
Jeremiah M.
PROVING A THEOREM To prove the Tangent and Intersected Chord Theorem (Theorem 10.14 ), you must prove three cases. a. The diagram shows the case where $\overline{A B}$ contains the center of the circle. Use the Tangent Line to Circle Theorem (Theorem 10.1) to write a paragraph proof for this case. b. Draw a diagram and write a proof for the case where the center of the circle is in the interior of $\angle \mathrm{CAB}$ c. Draw a diagram and write a proof for the case where the center of the circle is in the exterior of $\angle \mathrm{CAB}$
Circles
Angle Relationships in Circles
Recommended Textbooks
Geometry A Common Core Curriculum
Geometry
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD