## Abhisar one year ago Prove that length of the chord P1P2 is 2RCos $$\theta$$

1. Abhisar

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2. welshfella

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3. welshfella

By the Cosine Rule r^2 =r^2 +p1p2 ^2 - 2r(p1p2)cos theta solve for p1p2

4. welshfella

p1p2 ^2 - 2r(p1p2)cos theta r^2 - r^2 = 0 p1p2(p1p2 - 2r cos theta) = 0 (p1p2 - 2r cos theta) = 0 or pip2 = 0 p1p2 = 2r cos theta

5. welshfella

* correction to first line:- p1p2 ^2 - 2r(p1p2)cos theta = r^2 - r^2 = 0

6. Loser66

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7. Loser66

O is middle point of $$P_1P_2$$, and $$P_1C= R$$ Hence $$CO\perp P_1P_2$$, that gives us $$cos (\theta)=\dfrac{P_1O}{R}\rightarrow 2P_1O=P_1P_2= 2Rcos(\theta)$$

8. Abhisar

Thank you very much @welshfella and @loser66

9. Loser66