High School

We appreciate your visit to K L and M are points on the circle KS is a tangent to the circle at K KM is a diameter and triangle KLM. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

K, L, and M are points on the circle. KS is a tangent to the circle at K. KM is a diameter and triangle KLM is isosceles. Find the value of z.

K L and M are points on the circle KS is a tangent to the circle at K KM is a diameter and triangle KLM

Answer :

Using the circle theorems, the value of z is 45

Circle Geometry

From the question, we are to determine the value of z

From the given information,

KM is a diameter

∴ ∠KLM = 90° (Angle in a semicircle)

Also, ΔKLM is isosceles

∴ ∠KML = ∠MKL (Base angles of an isosceles triangle)

Then,

∠KML + ∠MKL + ∠KLM = 180° (Sum of angles in a triangle)

2× ∠KML + 90° = 180°

2× ∠KML = 180° - 90°

2× ∠KML = 90°

∠KML = 90°/2

∠KML = 45°

Now, we can observe that

z° = ∠KML (Angles in alternate segment)

But,

∠KML = 45°

∴ z = 45

Hence, the value of z is 45

Learn more on Circle Geometry here: https://brainly.com/question/17074363

#SPJ1

Thanks for taking the time to read K L and M are points on the circle KS is a tangent to the circle at K KM is a diameter and triangle KLM. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada