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Mathematics

Coordinate-Geometry

Easy

Question

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

$Length of RS = \frac{\sqrt{7}}{2}$
$Length of OE = \frac{1}{6}$
$Radius of incircle of ΔPQR = \frac{\sqrt{3}}{2} (2 - \sqrt{3})$
$Area of ΔSOE = \frac{\sqrt{3}}{12}$

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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