Finding angle of a reflected isosceles triangle

  • #1
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0

Homework Statement


I am trying to find the following (marked in red) angle, I know that the radii to the points of contact make an angle θ with the horizontal.

2me5pw0.jpg



Homework Equations


all angles of a triangle add up to 180 degrees.
isosceles triangle, has two equivalent sides


The Attempt at a Solution


5l0yv8.png


I tried using symmetry and found the part in red is [itex]\pi[/itex] - 2[itex]\theta[/itex]
but according to the text, the angle is 2[itex]\theta[/itex]. I am confused on why is is 2[itex]\theta[/itex]
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
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The sides of the inverted triangle are tangents to each circle.
The base of your blue triangle is 2R.
The angles on either side of the base must be ##\theta##.

The blue-triangle apex angle must be ##\pi-2\theta## ... which is where you've got up to.

The apex of the blue triangle forms a diamond shape with the inverted triangle.
The bottom of the diamond is the angle you want.
The left-hand angle is the same as the right-hand angle - you actually know what these angles are!

What do the angles in the diamond add up to?
What do the left hand and right hand angles add up to?
 

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