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## Class 9 (Assamese)

### Course: Class 9 (Assamese)>Unit 10

Lesson 2: Angle subtended by a chord/arc of a circle

# Inscribed angle theorem proof

Proving that an inscribed angle is half of a central angle that subtends the same arc. Created by Sal Khan.

## Want to join the conversation?

• Could you do a problem like this with different variables?
Like, instead of Psi and Theta, could you use x and y? •   Yes, you can use whichever variables you like. But x and y are commonly used to indicate lengths, and psi and theta are commonly used to indicate angles, so that's what Sal has done.
• At how do you know psi 1 is = to 1/2 beta 1, and same for psi 2 and beta 2? •  At minutes of this video Sal proves psi = 1/2 beta when one ray is a diameter, in the example you're asking about he creates a diameter so he can use this result to know Psi 1 = 1/2 beta 1 and the same for psi 2 and beta 2.
• I had a question about theta. If someone draws the symbol theta would you draw the line that goes in the center only as long as the radus or to the diameter? Thank you very much. • Theta is simply a variable that he uses to describe one of the two types of angles used in the above video: central angles. The symbol theta has no meaning specific to the concept discussed in the above video; like Psi, which he uses to indicate the inscribed angles, the Theta symbol is used to represent something, therefore it is not how the symbol is drawn that matters--it is what the symbol represents that matters.
• At and , Sal says "vertex", what does that mean? • The Vertex is the point where the two line segments meet. So at when he points to the vertex he is staying, the place where the two line segments meet, which is on the circumference of the circle
• Wait, in that third situation, what garuntee do you have that si 2 = theta 2? There are three triangles in that part of the video (at ) and in the other parts, then there are two triangles? It doesn't really make much sense. • he's taking from the first example- if one of the chords of the angle is the diameter then we already know that psi= 1/2theta, we already proved that. so using that we know that psi2=½(theta2) and we can and since the huge angle we made also has one of the chords on the diameter, we can state that psi1+psi2=½(theta1+theta2). Since we know that psi2=1/2theta1, we can plug it in and now we have psi1+1/2theta1=½theta1 +½ theta2 and the term 1/2theta1 cancels from both sides and you are left with psi1=1/2theta1, which are the two measurements we were looking for.Hope this helps.
• I don't get it... why not just use X or Z? • Learning Proofs are the best. I find they are often better than practice questions for remembering a theorem.Is there like a course on proofs on Khan Academy? • I still don't understand really much am still struggling to do the math need help.   