Two circles with radii r1 and r2- r 1 - r 2 - 2- touch each other externally- If - - be the angle between direct common tangents- then

The correct option is C α =sin ^ 1 ( r _ 1 r _ 2 r _ 1 + r _ 2 ) From the above image.In Δ DEC , DE / EC =sinα ⇒ r _ 2 sinα #160; =E ...

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Area Using Sine Rule

Two circles w...

Question

Two circles with radii $r_{1}$ and $r_{2},$ $r_{1} > r_{2} \geq 2$ , touch each other externally. If $^{'} α^{'}$ be the angle between direct common tangents, then

α = {sin}^{- 1} (\frac{r_{1} + r_{2}}{r_{1} - r_{2}})

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α = 2 {sin}^{- 1} (\frac{r_{1} - r_{2}}{r_{1} + r_{2}})

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α = {sin}^{- 1} (\frac{r_{1} - r_{2}}{r_{1} + r_{2}})

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α = {sin}^{- 1} (\frac{r_{1}}{r_{2}})

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Let $c_{1} & c_{2}$ be the centers and $r_{1} & r_{2}$ be the radius of two circles. Then

Cases Conditions

p. 1. $| r_{1} - r_{2} | < c_{1} c_{2} < r_{1} + r_{2}$

q. 2. $| r_{1} - r_{2} | = c_{1} c_{2}$

r. 3. $c_{1} c_{2} < | r_{1} + r_{2} |$

4. $r_{1} + r_{2} < c_{1} r_{2}$

t. 5. $r_{1} + r_{2} = c_{1} r_{2}$

r_{1}, r_{2}, r_{1}^{'}

r_{2}^{'}

r_{1}

r_{2}

C_{1}, C_{2}

C_{3}

r_{1}, r_{2}

r_{1} + r_{2}

C_{1}

C_{2}

C_{3}

r_{3}

r_{1} > r_{2} > r_{3}

r_{1}, r_{2}, r_{3}

{(\frac{r_{1}}{r_{2}})}^{3}

R_{1} - C \equiv N + R_{2} M g B r (i) D r y e t h e r - ------ \to (i i) H_{3} O^{+} 1 - p h e n y l - 1 - p r o p a n o n e

R_{1}

R_{2}

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