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# Tangents of circles problem (example 3)

CCSS.Math:

## Video transcript

line AC is tangent to circle o at Point C so this is line AC tangent to circle o at Point C what is the length of segment AC what is this distance right over here between point a and Point C I encourage you now to pause this video and try this out on your own so I'm assuming you've given a go at it so the key thing to realize here if since AC is tangent to the circle at Point C that means it's going to be perpendicular to the radius between the center of the circle and Point C so this right over here is a right right angle and the reason why that is useful is now we know that triangle a OC is a right triangle so we could use if we know two of its sides we could use the Pythagorean theorem to figure out the third now we clearly know Oh see now Oh a we don't know the entire side they only give us that a B is equal to two but the thing that might jump out at your in your mind is OB is a radius OB is a radius it's going to be the same length as any radius so this is going to be three as well so the distance between the center of the circle and a point on the circle just like the distance between o and C so this is going to be three as well and so now we are able to figure out that the hypotenuse of this triangle has length 5 and so we need to figure out what side the slot the length of segment AC is so let's just call that I don't know I'll call that I will call that X X and so we know that x squared plus 3 squared I'm just applying the Pythagorean theorem here so plus 3 squared is going to be equal to the length of the hypotenuse squared is going to be equal to 5 squared and I know this is the hypotenuse it's the side opposite the 90 degree angle it's the longest side of the right triangle so x squared x squared plus 9 plus 9 is equal to 25 is equal to 25 subtract 9 from both sides and you get you get x squared is equal to 16 and so it should jump out at you that X is going to be equal to X is equal to 4 so X is equal to 4 X is the same thing as the length of segment AC so the length of segment AC is 4