Mathematics
Coordinate-Geometry
Easy

Question

I n space a space n o n minus r i g h t minus a n g l e d space t r i a n g l e space increment P Q R comma space l e t space p comma space q comma space r space d e n o t e space t h e space l e n g h t s space o f space t h e space s i d e s space o p p o s i t e space t o space t h e space a n g l e s space a t space P comma space Q comma space R space r e s p e c t i v e l y. space T h e space m e d i a n space f r o m space R space m e e t s space t h e space s i d e space P Q space a t space S comma space t h e space p e r p e n d i c u l a r space f r o m space P space m e e t s space t h e space s i d e space Q R space a t space E space a n d space R S space a n d space P E space i n t e r s e c t space a t space O. space I f space p equals square root of 3 comma space q equals 1 comma space n d space t h e space r a d i u s space o f space t h e space c i r c u m c i r c l e space o f space t h e space increment P Q R space e q u a l s space 1 comma space t h e n space w h i c h space o f space t h e space f o l l o w i n g space o p t i o n s space i s divided by a r e space c o r r e c t space ?

  1. text  Length of  end text RS equals fraction numerator square root of 7 over denominator 2 end fraction
  2. text  Length of  end text OE equals 1 over 6
  3. text  Radius of incircle of  end text straight capital delta PQR equals fraction numerator square root of 3 over denominator 2 end fraction left parenthesis 2 minus square root of 3 right parenthesis
  4. text  Area of  end text straight capital delta SOE equals fraction numerator square root of 3 over denominator 12 end fraction

The correct answers are: text  Radius of incircle of  end text straight capital delta PQR equals fraction numerator square root of 3 over denominator 2 end fraction left parenthesis 2 minus square root of 3 right parenthesis, text  Length of  end text OE equals 1 over 6, text  Length of  end text RS equals fraction numerator square root of 7 over denominator 2 end fraction

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text  A rectangle is inscribed in a circle with a diameter lying along the line   end text 3 y equals x plus 7. text  If the two adjacent vertices   of the  end text
text rectangle are  end text left parenthesis negative 8 comma 5 right parenthesis text  and  end text left parenthesis 6 comma 5 right parenthesis comma text  then the area of the rectangle (in sq. units) is :  end text space

text  A rectangle is inscribed in a circle with a diameter lying along the line   end text 3 y equals x plus 7. text  If the two adjacent vertices   of the  end text
text rectangle are  end text left parenthesis negative 8 comma 5 right parenthesis text  and  end text left parenthesis 6 comma 5 right parenthesis comma text  then the area of the rectangle (in sq. units) is :  end text space

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