Relation between Exradius-semiperimeter and circumradius can be given by r 1 is the radius of the circle opposite the angle A A- r1-2 -s-a- r1-4 R cosA-2sinB-2sinC-2B- r 1-s- a - r 1-4 R sin A -2cos2-2 cos 2C- r1-5-a2-s-as-b- r1-4 R cosA-2sin2-2sinC-2D- r1-s-a-s-bs-c- r1-4 R cosA-2sinB-2sinC-2

The correct option is B r_1=Δ/s a,r_1=4R sinA/2 cosB/2 cos C/2Relation between Exradius and semiperimeter can be given by, r_1=Δ/s a where r_1 is the radius ...

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Standard XII

Mathematics

Ex Radius

Relation betw...

Question

Relation between Exradius ,semiperimeter and circumradius can be given by
( $r_{1}$ is the radius of the circle opposite the angle A)

r_{1} = \frac{2 Δ}{s - a}, r_{1} = 4 R c o s \frac{A}{2} s i n \frac{B}{2} s i n \frac{C}{2}

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r_{1} = \frac{Δ}{s - a}, r_{1} = 4 R s i n \frac{A}{2} c o s \frac{B}{2} c o s \frac{C}{2}

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r_{1} = \frac{2 Δ}{(s - a) (s - b)}, r_{1} = 4 R c o s \frac{A}{2} s i n \frac{B}{2} s i n \frac{C}{2}

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r_{1} = \frac{Δ (s - a)}{(s - b) (s - c)}, r_{1} = 4 R c o s \frac{A}{2} s i n \frac{B}{2} s i n \frac{C}{2}

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Solution

The correct option is B $r_{1} = \frac{Δ}{s - a}, r_{1} = 4 R s i n \frac{A}{2} c o s \frac{B}{2} c o s \frac{C}{2}$
Relation between Exradius and semiperimeter can be given by, $r_{1} = \frac{Δ}{s - a}$ where $r_{1}$ is the radius of the circle opposite the angle A. and it's helpful to remember the identity $r_{1} = 4 R s i n \frac{A}{2} c o s \frac{B}{2} c o s \frac{C}{2}$

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Similar questions

Q. Relation between Exradius ,semiperimeter and circumradius can be given by
(

r_{1}

is the radius of the circle opposite the angle A)

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

A projectile thrown at an angle of $30^{\circ}$ with the horizontal has a range $R_{1}$ . Another projectile thrown, with the same velocity, at an angle $30^{\circ}$ with the vertical, has a range $R_{2}$ . The relation between $R_{1}$ and $R_{2}$ is

For the relation $R_{1}$ defined on R by the rule $(a, b) ϵ R_{1} \Leftrightarrow 1 + a b > 0.$

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$\Rightarrow (a, c) ϵ R_{1}$ is not true for all $a, b c ϵ R$

Q. For the relation R₁ defined on R by the rule (a, b) ∈ R₁ ⇔ 1 + ab > 0.
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Relation between Exradius ,semiperimeter and circumradius can be given by (r1 is the radius of the circle opposite the angle A)

The correct option is B r1=Δs−a,r1=4RsinA2cosB2cosC2Relation between Exradius and semiperimeter can be given by, r1=Δs−a where r1 is the radius of the circle opposite the angle A. and it's helpful to remember the identity r1=4RsinA2cosB2cosC2

Relation between Exradius ,semiperimeter and circumradius can be given by
( $r_{1}$ is the radius of the circle opposite the angle A)