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# Tangents of circles problem (example 1)

Sal finds missing angles using the property that tangents are perpendicular to the radius.

## Want to join the conversation?

• So the opposite angles of a quadrilateral are supplementary.
Would that be proof of the first answer? Or is the first answer proof of that fact? Because I'll be honest, I try not to just jump to the easy answer when I'm learning a new concept - but the answer to the first question was practically reflex.
• The opposite angles of a quadrilateral are not necessarily supplementary. The only condition on the angles is that all four of them must sum to 360˚.

If the opposite angles do happen to be supplementary, however, some interesting properties arise. One such property is that such a quadrilateral must be cyclic (that is, it must be inscribable in a circle).
• How did you get that 50 on that sec problem
• Because since the degree measure of a minor arc is the same as its central angle, and Sal's central angle was 100, Arc BC was = 100. And since an inscribed angle's degree measure is 1/2 of the minor arc it intercepts, and D intercepts Arc BC, D = 50.
• What does it mean when a line is "tangent to a circle?"
• That it touches the circle at one and only one point. With this, it can be shown that a radius drawn to the point of tangency will be perpendicular to the line of tangency.
• so at what's basically happening is that an angle at the center of the circle is double the angle made anywhere else on the circle, and conversely the angle anywhere else on the circle would be double the angle at the angle at the center.
• Yes you are correct. It is a theorem, the inscribed angle is half of the central angle if and only if they are on the same arc.
• instead of making it long a little long can I use the statement : "the opposite angles in a quadrilateral are equal to 180" so I can directly subtract 80 from 180 which will give me 100, which is angle COB.
• not all quadrilaterals will have opposite angles equal to 180. but you can use the angle sum property of quadrilaterals is 360.

here, the radii make 90 degree angles with the tangents thus, the opposite angles make 180.
• couldn't you just to 92+x=180 and not do the extra steps when you do 92+180+x=360?
(1 vote)
• Yes, you can, but you have to make sure you don't mess up your information when you make this shortcut.
the extra information helps you understand how the problem works.
I hope this helps. :)
• why the tangent line is different the other line