Math Question and Answers


Question and Answers Forum

All Questions Topic List
Mensuration Questions
Previous in All Question Next in All Question
Previous in Mensuration Next in Mensuration
Question Number 91836 by M±th+et+s last updated on 03/May/20

Commented by M±th+et+s last updated on 03/May/20

$l e t A B C D b e f o u r p o i n t s o n a c i r c l e$ $l e t f o u r m o r e c i r v c e s p a s s t h r o u g h$ $A B, B C, C D, D A R e s p e c t i v e l y,$ $m e e t i n g i n f u r t h e r p o i n t s P, Q, R, S .$ $s h o w t h a t P, Q, R a n d S a r e c o n s y c l i c .$
	Answered by mr W last updated on 04/May/20

	Commented by mr W last updated on 04/May/20

	Commented by mr W last updated on 07/May/20

	$α_{1} + α_{4} = α_{2} + α_{3} = π, s i n c e A B Q P i s c y c l i c .$ $β_{1} + β_{4} = β_{2} + β_{3}$ $γ_{1} + γ_{4} = γ_{2} + γ_{3}$ $δ_{1} + δ_{4} = δ_{2} + δ_{3}$ $(α_{1} + δ_{2}) + (α_{4} + δ_{3}) = (α_{2} + δ_{1}) + (α_{3} + δ_{4})$ $(β_{2} + γ_{1}) + (β_{3} + γ_{4}) = (β_{1} + γ_{2}) + (β_{4} + γ_{3})$ $(α_{1} + δ_{2} + β_{2} + γ_{1}) + (α_{4} + δ_{3} + β_{3} + γ_{4}) = (γ_{2} + δ_{1} + α_{2} + β_{1}) + (α_{3} + δ_{4} + β_{4} + γ_{3})$ $α_{4} + β_{3} + γ_{4} + δ_{3} = α_{3} + δ_{4} + β_{4} + γ_{3}$ $2 π - θ_{B} + 2 π - θ_{D} = 2 π - θ_{A} + 2 π - θ_{C}$ $\Rightarrow θ_{B} + θ_{D} = θ_{A} + θ_{C}$ $s i n c e θ_{A} + θ_{B} + θ_{C} + θ_{D} = 2 π$ $\Rightarrow θ_{B} + θ_{D} = θ_{A} + θ_{C} = π$ $i . e . P Q R S i s c y c l i c .$
	Commented by M±th+et+s last updated on 04/May/20

	$g r e a t w o r k s i r$
Terms of Service
Privacy Policy
Contact: info@tinkutara.com

Question and Answers Forum