Miriam69690
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What is the angle of measure of MBE?

What is the angle measure of SAE?

What can you say about the triangles MBE and SAE?

If SE=100 ME=5 and MB=2 find SA=?

What is the angle of measure of MBE What is the angle measure of SAE What can you say about the triangles MBE and SAE If SE100 ME5 and MB2 find SA class=


Answer :

Answer:

  • ∠MBE = 90°
  • ∠SAE = 90°
  • ΔMBE is similar to ΔSAE
  • SA = 40

Step-by-step explanation:

To find the angles of ∠MBE and ∠SAE, given AE is the tangent line of circle S and circle M, we have to understand this rule:

"The tangent line of a circle is perpendicular to the radius that passes through the tangent point."

Therefore:

  • ∠MBE = 90°
  • ∠SAE = 90°

Now, we compare ΔMBE and ΔSAE. Both triangles shares 2 pairs of same angles, which are:

  • ∠MBE = ∠SAE = 90°
  • ∠BEM = ∠AES (both angles overlap one another)

Hence, we can conclude that their 3rd angles must be the same ⇒ ∠BME = ∠ASE. Since both ΔMBE and ΔSAE have same corresponding angles, then ΔMBE and ΔSAE are similar triangles.

For similar triangles, the corresponding sides are in the same ratio:

[tex]\boxed{BE : AE = MB : SA = ME : SE}[/tex]

If SE = 100, ME = 5 and MB = 2, then:

[tex]\begin{aligned}MB:SA&=ME:SE\\2:SA&=5:100\\5\times SA&=2\times100\\SA&=200\div5\\\bf SA&=\bf40\end{aligned}[/tex]

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