Circle

#Geometry

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

$L.H.S=l(\sin(\theta)\cos(\phi)+\sin(\phi)\cos(\theta))=l \left(\dfrac{BC \cdot n}{l^2}+\dfrac{m \cdot DC}{l^2}\right)=\dfrac 1 l \left(BC \cdot n+DC \cdot m \right)$ .

$R.H.S= n \cdot \dfrac{BC}{l}+m \cdot \dfrac{CD}{l}=\dfrac 1 l \left(BC \cdot n+DC \cdot m \right)$ .

$L.H.S=R.H.S$ . Proved.

A Former Brilliant Member - 5 years ago

But it's not given that $AC$ is a diameter right?

A Former Brilliant Member - 5 years ago

I guess we have to assume that it is.

A Former Brilliant Member - 5 years ago

Ahmad Saad - 4 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$