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CBSE Class 9 Answered

ABCD is a cyclic quadrilateral in which AB is the diameter of the circle which is passing through A,B,C & D. If angle ADC is equal to 130°, find angle  BAC
 
Asked by saketh | 10 Feb, 2015, 07:15: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space f o l l o w i n g space d i a g r a m.
G i v e n space t h a t space A B C D space i s space a space c y c l i c space q u a d r i l a t e r a l space a n d space A B space i s space t h e space d i a m e t e r space o f space t h e space c i r c l e. A n d space h e n c e space o p p o s i t e space a n g l e s space a r e space s u p p l e m e n t a r y. A l s o space g i v e n space t h a t space angle A D C equals 130 degree T h e r e f o r e space angle A D C plus angle A B C equals 130 degree plus angle A B C equals 180 degree rightwards double arrow angle A B C equals 180 degree minus 130 degree equals 50 degree F r o m space t h e space d i a g r a m comma space i t space i s space c l e a r space t h a t space C space i s space i n space b e t w e e n space t h e space p o i n t s space A space a n d space B. W e space k n o w space t h a t space t h e space a n g l e space i n space a space s e m i space c i r c l e space i s space a space r i g h t space a n g l e. T h u s comma space angle A C B equals 90 degree W e space n e e d space t o space f i n d space angle B A C colon C o n s i d e r space t h e space r i g h t space t r t i a n g l e space comma space A B C T h u s comma space angle B A C plus space angle A C B plus angle A B C equals 180 degree rightwards double arrow space angle B A C plus space 90 degree plus 50 degree equals 180 degree rightwards double arrow space angle B A C equals 180 degree minus space 90 degree minus 50 degree rightwards double arrow space angle B A C equals 40 degree
Answered by Vimala Ramamurthy | 11 Feb, 2015, 10:13: AM

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CBSE 9 - Maths
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