The measure of AK, AL and KL are 19.66, 10.14 and 23.64 respectively
Circle Geometry
Given the following parameters
KAL=100, L=25, and OA=21.
Dtermine the measure of m∠AKL
m∠AKL = 180° - 100° - 25° = 55°
m∠AKL = 55 degrees
Since the line KL is a chord, hence the triangle in the circle is isosceles with AO = LO = 12
Given that ∠AOL is a central angle. ∠AKL is an inscribed angle, intersecting the same ark of the circle.
m∠AOL = 2(m∠AKL) = 2 * 55° = 110°
Using the Law of Cosines to determine the value of AL
AL = √(122 + 122 - 2•122•cos(110°) ≅ 19.659649
AL = 19. 66
Similarly for AK
AK = √(122 + 122 - 2•122•cos(50°)
AK ≅ 10.14
We will find the length of LK from ΔLAK.
LK = √(AL2 + AK2 - 2•AL•AK•cos(100°)
LK ≅ 23.64
Hence the measure of AK, AL and KL are 19.66, 10.14 and 23.64 respectively
Learn more on law of cosines here:https://brainly.com/question/7872492
