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ans is a,d
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Asked by jatinmankar | 17 May, 2019, 23:41: PM
answered-by-expert Expert Answer
G i v e n space l i n e s space a r e x over a plus y over b equals 1 space a n d space x over c plus y over d equals 1 T h e s e space t w o space l i n e s space i n t e r s e c t space a x e s space a t space f o u r space c o n c y c l i c space p o i n t s S o comma space t h e space f i r s t space l i n e space i n t e r s e t space a x e s space a t space left parenthesis a comma 0 right parenthesis space a n d space left parenthesis 0 comma b right parenthesis S i m i l a r l y comma space s e c o n d space l i n e space i n t e r s e c t space a t space left parenthesis c comma 0 right parenthesis space a n d space left parenthesis 0 comma d right parenthesis S i n c e space t h e space i n t e r s e c t i o n space p o i n t space o f space a space l i n e space a n d space a x e s space a r e space c o n c y c l i c space p o i n t s U sin g space p o w e r space o f space a space c i r c l e comma space w e space h a v e a c equals b d N o w comma space t h e space g i v e n space l i n e s space c a n space b e space r e w r i t t e n space a s b x plus a y equals a b space.... space left parenthesis i right parenthesis space a n d space d x plus c y equals c d space.... space left parenthesis i i right parenthesis S o l v i n g space left parenthesis 1 right parenthesis space a n d space left parenthesis i i right parenthesis space s i m u l a tan e o u s l y comma space w e space h a v e x equals fraction numerator a c left parenthesis b minus d right parenthesis over denominator b c minus a d end fraction S u b s t i t u t i n g space t h i s space v a l u e space i n space left parenthesis i right parenthesis comma space w e space h a v e y equals fraction numerator b d left parenthesis c minus a right parenthesis over denominator b c minus a d end fraction N o w comma space i t space i s space g i v e n space t h a t space a squared plus c squared equals b squared plus d squared rightwards double arrow a squared plus c squared minus 2 a c equals b squared plus d squared minus 2 a c rightwards double arrow a squared plus c squared minus 2 a c equals b squared plus d squared minus 2 b d space............ space S i c e comma space a c equals b d rightwards double arrow left parenthesis c minus a right parenthesis squared equals left parenthesis b minus d right parenthesis squared rightwards double arrow left parenthesis c minus a right parenthesis equals plus-or-minus left parenthesis b minus d right parenthesis I f space space c minus a equals b minus d space rightwards double arrow x equals y I f space c minus a equals negative left parenthesis b minus d right parenthesis space rightwards double arrow x equals negative y S o space t h e space l i n e s space c a n space i n t e r s e c t space a t space left parenthesis 1 comma 1 right parenthesis comma space left parenthesis 1 comma negative 1 right parenthesis comma space left parenthesis 2 comma negative 2 right parenthesis space left parenthesis 3 comma 3 right parenthesis A l l space f o u r space o p t i o n s space a r e space t r u e.
Answered by Renu Varma | 18 May, 2019, 10:23: AM

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