Question

Given: KAL=100, L=25, and OA=21. Find: AK,AL, and KL

Answer 1

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:brainly.com/question/7872492