Let P be a point outside the circle such that triangle LMP has legs coincident with chords MW and LK (i.e. M, W, and P are colinear, and L, K, and P are colinear). By the intersecting secants theorem,
![m\angle LPM=\dfrac{m\widehat{LM}-m\widehat{WK}}2\impliesm\angle LPM=48^\circ](https://tex.z-dn.net/?f=m%5Cangle%20LPM%3D%5Cdfrac%7Bm%5Cwidehat%7BLM%7D-m%5Cwidehat%7BWK%7D%7D2%5Cimpliesm%5Cangle%20LPM%3D48%5E%5Ccirc)
The angles in any triangle add to 180 degrees in measure, and
and
, so that
![m\angle MLK+m\angle LPM+m\angle LMP=180^\circ](https://tex.z-dn.net/?f=m%5Cangle%20MLK%2Bm%5Cangle%20LPM%2Bm%5Cangle%20LMP%3D180%5E%5Ccirc)
![\implies\boxed{m\angle LMW=67^\circ}](https://tex.z-dn.net/?f=%5Cimplies%5Cboxed%7Bm%5Cangle%20LMW%3D67%5E%5Ccirc%7D)
Answer:
If your question is set up like this
then your answer is No solution.
If your question is set up like this
then your answer is
or x = 0.765
Hope this helps!
Answer:
Lindsey, who is delivering her speech in a large auditorium
Step-by-step explanation:
Jin, who is delivering her speech to a small group sitting around a table
Lindsey, who is delivering her speech in a large auditorium
Luke, who is delivering his speech in a typical classroom
Jordan, who is delivering his speech in a small meeting room
Answer: 120 ft
<u>Step-by-step explanation:</u>
The Ellipse equation is:
where
- (h, k) is the center
- "a" is the horizontal radius
- "b" is the vertical radius
- c is the distance from the center to the foci: |a² - b²| = c²
Given: horizontal diameter = 122 → horizontal radius = 61 = a
vertical diameter = 22 → vertical radius = 11 = b
Foci (c): 61² - 11² = c²
3721 - 121 = c²
3600 = c²
±60 = c
Let (h, k) = (0, 0)
Then the foci are located at -60 and +60.
The distance between them is 60 + 60 = 120