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### Course: Class 10>Unit 10

Lesson 3: Circles 10.2

# Proof: Segments tangent to circle from outside point are congruent

Sal proves that two tangent segments to a circle that are drawn from the same outside point are congruent.

## Want to join the conversation?

• I tried to make my own proof, is this valid? If you draw a line connecting each "tangent point" you will get another triangle, and now I had the 3rd angle so I put it as an equation 2x + 73 (that is the third angle) = 180, solved that which told me that the base angles are corresponding angles which means it must be an isosceles triangle, thus the lines are congruent.
• Actually, no. If you construct a triangle by drawing a line connecting the tangent points of the circle, the only way you could get that "2x" term in your equation is if you already assume that the triangle is isosceles (so that 2 of the 3 angles and 2 of the 3 sides would be congruent), which would directly imply the congruence of the tangent lines. To put it namely, your proof contains a fallacy: affirming the consequent, and it's therefore invalid.
• this dont make no sense
• But that means it makes sense; double negative.
• What property proves that the hypotenuses of the two right triangles are congruent?
• If they are the same line, you can use the Reflexive property to prove that they are congruent. If you can prove that the triangles are congruent, then the hypotenuses are also congruent. Also, the problem sometimes tells you that they are congruent.
• So just to check, a tangent line is a line that touches a circle at only one point right?
• Yes, a tangent line just touches a curve (in this video it is the curve of a circle) at only one point.
• if the point o which is inside the circle is 117 degrees then would it double to figure out the measure of angle A?
• We are told that angles B and C are right angles, which add up to equal 180°. Since the angles in a quadrilateral add up to 360°, angle o plus angle A equal 360-180=180°. If, as you say, angle o is 117°, then angle A has to be 180-117=63°. Was that what you were asking?
• The size of the line doesn't matter though in terms of congruency? (I nearly said congruenchy like crunchy 🍪).
• It does, for it to be congruent it must be the same size
(1 vote)
• Can I also use the RSH postulate instead of the Hypotenuse Leg Theorem?
(1 vote)
• They are the same thing. HL, hypotenuse is only defined for a right triangle, so you need a right angle, the hypotenuse, and one of the legs.
RSH means right triangle, you need one of the sides and the hypotenuse.
The only difference is that one calls it a side and the other calls it a leg.
(1 vote)
• Doesn't the Side Side Side Theorem prove that the hypotenuses of the 2 right triangle are congruent?
(1 vote)
• Yes, it could, but there are more ways to prove that 2 hypotenuses are congruent.
(1 vote)
• wouldn't you be able to use ssa congruency instead of hypotenuse leg congruency ?