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GeometryQuestion and Answers: Page 13

Question Number 205062 Answers: 3 Comments: 0

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The figure below represents a design on the windows of a building. The curved part XY is an arc of a circle. The rise of the segmental arc is 10cm, its span is 100cm and XZ=ZY=120cm. calculate: (i) the radius of the circle (ii) the area of the segmental cap, correct to 2 significant figures. (iii) the total area of the design, correct to 3 significant figures.

$T h e f i g u r e b e l o w r e p r e s e n t s a d e s i g n$ $o n t h e w i n d o w s o f a b u i l d i n g . T h e$ $c u r v e d p a r t X Y i s a n a r c o f a c i r c l e .$ $T h e r i s e o f t h e s e g m e n t a l a r c i s 10 c m,$ $i t s s p a n i s 100 c m a n d X Z = Z Y = 120 c m .$ $c a l c u l a t e :$ $(i) t h e r a d i u s o f t h e c i r c l e$ $(i i) t h e a r e a o f t h e s e g m e n t a l c a p,$ $c o r r e c t t o 2 s i g n i f i c a n t f i g u r e s .$ $(i i i) t h e t o t a l a r e a o f t h e d e s i g n, c o r r e c t$ $t o 3 s i g n i f i c a n t f i g u r e s .$

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In a regular pentagon PQRST , PR intersects QS at O. Calculate ROS?

$I n a r e g u l a r p e n t a g o n P Q R S T, P R$ $i n t e r s e c t s Q S a t O . C a l c u l a t e R O S ?$

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