So if this is a 100 degree measured arc, then the measure of this angle right over here is going to be 50 degrees. Videos that an inscribed angle that intercepts that arc is going to have half the arc's measure. That's an inscribed angle that intercepts the same arc. And so if we're trying to find this angle, the measure of angle D, intercepts arc C, B, right over here, that tells us that the measure of arc C, B, is also 100 degrees. The measure of this arc cause that interior angle intercepts. Sides, we get Y is equal to 100 or the measure of this is 100, the measure of this interior angle right over here is 100 degrees, which also tells us that
#Chord geometry diagram plus#
And so let's see you have, we could have Y plus 80 is equal to 180, if I just subtract 180 from both sides if I subtract 80 from both
To be equal to 360 degrees sum of the interiorĪngles of a quadrilateral. Plus 90, so I could say plus another 180 is going
So we have Y plus 80 degrees or we'll just assumeĮverything is in degrees, so Y plus 80 plus 90 Of the central angle let's call that Y over there. We saw in the last question, this angle, plus thisĪngle, plus this angle, plus the central angle are And then this would be a right angle and so by the same logic as Intersecting with a tangent, or part of a tangent Quadrilateral A, B, O, C and we know two of the angles, we know this is going to be a right angle we have a radius So what can we figure out? Well just like in the last question we have a quadrilateral here, We want to find the measure of that angle and let's call that, In the last question and they said what is So it says, angle A isĬircumscribed about circle O, we have seen that before To subtract two more so it's going to be X is equals to 88. See 180 minus 90 would be 90 and then we're just going Subtract 180 from both sides and so, if we do that we would have 92 plus X is equals to 180 and if we subtract 92 from both sides we get X is equals to let's Plus X, they all have toĪdd up to be 360 degrees so let's see, we could So this is 92 + 90 + 90 + question mark is going to be equal to 360 degrees. Since you have two of them, it's 360 degrees. Quadrilateral into two triangles, where the sum of all the interior angles of a triangle are 180 and The sum of the angles are going to add up to 360 degrees, and if you wonder where that comes from well you can divide a So let me label this, so this is going to be a right angle and this is going to be a right angle. Perpendicular to a tangent or a radius that intersects a tangent is going to be perpendicular to it. This is to realize, that a radius is going to be So the key insight hereĪnd there's multiple ways that you could approach This out right here and I encourage you to pause the video and figure it out on your own. So given all of that they're asking us what is the measure of angle A, so we're trying to figure So you see that the sides of angle A are parts of those tangents,Īnd points B and point C are where those tangentsĪctually sit on the circle.
Line is tangent to the circle and (mumbles) and this line is also And when they say it'sĬircumscribed about circle O that means that the two sides of the angle they're segments that wouldīe part of tangent lines, so if we were to continue, so for example that right over there, that So this is angle A right over here, we're talking about thisĪngle right over there. Told that angle A is circumscribed about circle O.
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