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Properties Of Triangles

TS EAMCET 2020 (Online) 11th September Morning Shift

MCQ+1 / -02020

In a $\triangle A B C$, let $a, b, c, s, r, R, I, S, r_1, r_2, r_3$ stand for their usual meaning. Then Match the items of List-I with those of the items of List-II.
























































List-IList-II
A.

tan

⁡

<mi>A</mi>

<mn>2</mn>


=

<mi>r</mi>

<mrow>

  <mi>s</mi>

  <mo>−</mo>

  <mi>a</mi>

</mrow>




tan

⁡

<mi>A</mi>

<mn>2</mn>


=

<mi>r</mi>

<mrow>

  <mi>s</mi>

  <mo>−</mo>

  <mi>a</mi>

</mrow>


tan((A)/(2))=(r)/(s-a)		I.

(

A

l

)

<mo data-mjx-texclass="OPEN">(</mo>

<mfrac>

  <msqrt>

    <mo stretchy="false">(</mo>

    <mi>s</mi>

    <mo>−</mo>

    <mi>b</mi>

    <mo stretchy="false">)</mo>

    <mo stretchy="false">(</mo>

    <mi>s</mi>

    <mo>−</mo>

    <mi>c</mi>

    <mo stretchy="false">)</mo>

  </msqrt>

  <mrow>

    <mi>b</mi>

    <mi>c</mi>

  </mrow>

</mfrac>

<mo data-mjx-texclass="CLOSE">)</mo>




(

A

l

)

<mrow>

  <mfrac>

    <msqrt>

      <mo stretchy="false">(</mo>

      <mi>s</mi>

      <mo>−</mo>

      <mi>b</mi>

      <mo stretchy="false">)</mo>

      <mo stretchy="false">(</mo>

      <mi>s</mi>

      <mo>−</mo>

      <mi>c</mi>

      <mo stretchy="false">)</mo>

    </msqrt>

    <mrow>

      <mi>b</mi>

      <mi>c</mi>

    </mrow>

  </mfrac>  

</mrow>


(Al)((sqrt((s-b)(s-c)))/(bc))
B.

r



r

r		II. 

<mi>R</mi>

<mn>2</mn>




<mi>R</mi>

<mn>2</mn>


R^(2)
C.

(

S

I

<mo stretchy="false">)</mo>

<mn>2</mn>


+

2

R

r



(

S

I

<mo stretchy="false">)</mo>

<mn>2</mn>


+

2

R

r

(SI)^(2)+2Rr		III.

(

4

R

+

r

+

<mn>2</mn>


<mtext> </mtext>

<mi mathvariant="normal">s</mi>


)

(

4

R

+

r

−

<mn>2</mn>


<mtext> </mtext>

<mi mathvariant="normal">s</mi>


)



(

4

R

+

r

+

<mn>2</mn>


<mtext></mtext>

<mi mathvariant="normal">s</mi>


)

(

4

R

+

r

−

<mn>2</mn>


<mtext></mtext>

<mi mathvariant="normal">s</mi>


)

(4R+r+sqrt2s)(4R+r-sqrt2s)
D. 

<mi>r</mi>

<mn>1</mn>

<mn>2</mn>


+

<mi>r</mi>

<mn>2</mn>

<mn>2</mn>


+

<mi>r</mi>

<mn>3</mn>

<mn>2</mn>




<mrow>

  <mi>r</mi>

</mrow>

<mn>1</mn>

<mn>2</mn>


+

<mrow>

  <mi>r</mi>

</mrow>

<mn>2</mn>

<mn>2</mn>


+

<mrow>

  <mi>r</mi>

</mrow>

<mn>3</mn>

<mn>2</mn>


r_(1)^(2)+r_(2)^(2)+r_(3)^(2)		IV.

Rr

<mo>/</mo>


<mi mathvariant="normal">S</mi>




Rr

<mo>/</mo>


<mi mathvariant="normal">S</mi>


Rr//S
V. 

<mrow>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>b</mi>

  <mo stretchy="false">)</mo>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>c</mi>

  <mo stretchy="false">)</mo>

</mrow>

<mi mathvariant="normal">Δ</mi>




<mrow>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>b</mi>

  <mo stretchy="false">)</mo>

  <mo stretchy="false">(</mo>

  <mi>s</mi>

  <mo>−</mo>

  <mi>c</mi>

  <mo stretchy="false">)</mo>

</mrow>

<mi mathvariant="normal">Δ</mi>


((s-b)(s-c))/(Delta)

\(\text { The correct match is }\)

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