Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 9 Answered

in a triangle ABC angle A is 60 and the altitudes from. B and C meet AC and AB at P and Q and intersect each other at I prove that APIQ and PQBC are cyclic quadrilaters
Asked by chaturvedi.pragya2000 | 13 Mar, 2015, 01:54: PM
answered-by-expert Expert Answer
C o n s i d e r space t h e space f o l o w i n g space f i g u r e.
C o n s i d e r space t h e space t r i a n g l e s space triangle A B P space a n d space triangle A C Q W E space k n o w space t h a t space a n g l e s space angle B P A space equals space angle C Q A equals 90 degree T h e r e f o r e comma angle A B P equals 90 degree minus angle B A P equals 90 degree minus 60 degree equals 30 degree a n d angle A C Q equals 90 degree minus angle C A Q equals 90 degree minus 60 degree equals 30 degree C o n s i d e r space t h e space t r i a n g l e s space triangle B I Q space a n d space triangle C I P W e space k n o w space t h a t space a n g l e s space angle B Q I space equals space angle C P I equals 90 degree T h e r e f o r e comma angle B I Q equals 90 degree minus angle I B Q equals 90 degree minus angle A B P equals 90 degree minus 30 degree equals 60 degree a n d angle C I P equals 90 degree minus angle I C P equals 90 degree minus angle A C Q equals 90 degree minus 30 degree equals 60 degree S i n c e space v e r t i c a l l y space o p p o s i t e space a n g l e s space a r e space e q u a l comma space angle Q I P equals angle B I C... left parenthesis 1 right parenthesis T h e space a n g l e space a r o u n d space a space p o i n t space i s space 360 degree T h u s space t h e space a n g l e space a r o u n d space I equals 360 degree rightwards double arrow angle B I Q plus angle B I C plus angle C I P plus space angle P I Q equals 360 degree rightwards double arrow 60 degree plus angle B I C plus 60 degree plus space angle P I Q equals 360 degree rightwards double arrow 120 degree plus 2 angle B I C equals 360 degree space space space space space space space space space space space left square bracket f r o m space e q u a t i o n space left parenthesis 1 right parenthesis right square bracket rightwards double arrow 2 angle B I C equals 360 degree minus 120 degree rightwards double arrow 2 angle B I C equals 240 degree rightwards double arrow angle B I C equals fraction numerator 240 degree over denominator 2 end fraction rightwards double arrow angle B I C equals 120 degree rightwards double arrow space angle Q I P equals angle B I C equals 120 degree space space space space space space..... left parenthesis 2 right parenthesis N o w space c n s i d e r space t h e space q u a d r i l a t e r a l space A Q I P. angle A equals 60 degree space a n d space angle Q I P equals 120 degree space rightwards double arrow angle A plus space angle Q I P equals 60 degree plus 120 degree equals 180 degree A l s o comma space angle A Q I plus angle A P I equals 90 degree plus 90 degree equals 180 degree T h e r e f o r e comma space t h e space q u a d r i l a t e r a l space A Q I P 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.
Answered by Vimala Ramamurthy | 14 Mar, 2015, 10:40: AM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 9 - Maths
if the diameter AD of a circle is 34 cm and the length of a chord AB is 30 cm. what is the distance of AB from the ce
Asked by indu.suresh1220 | 27 Dec, 2023, 11:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
prove that of all chords of circle through a given point within it, the chord which is bisected at that point is the smallest
Asked by subbusuchi1978 | 05 Nov, 2023, 10:24: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
if two circles intersect at two points prove that their centres lie in the perpendicular bisector of the common chord
Asked by rameshsonkar1234ramesh | 21 Dec, 2022, 11:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
AB is chord of a circle with centre O. Let P and T be two points on the circumpherence such that < APB # < ATB and < APB = 80 degree then what is the value of < ATB.
question image
Asked by sdmbotch1123 | 17 Dec, 2022, 09:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
prove that the median bisecting the hypotenuse of a right angled triangle is half of the hypotenuse
Asked by geetaradha8835 | 16 Dec, 2022, 07:59: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
solution
question image
Asked by rairai4971 | 11 Jun, 2022, 09:03: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
three girls Reshma Salma And Mandeep are playing a game by standing on a circle of radius 5 drawn in a park Reshma throws a ball to Salma Salma To mandip mandip to Reshma if the distance between Reshma and Salman and between Salman Mandeep 6 each what is the distance between Reshma Mandip
Asked by chalkekalyani80 | 06 Mar, 2022, 11:25: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that equal chords of a circle subtend equal angles at the centre.
Asked by sangeetabharti123456789 | 22 Feb, 2022, 09:01: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
What is a tangent?
Asked by manognareddy.p28 | 25 Jul, 2021, 12:52: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 9 - Maths
Prove that the angle at the centre of a circle is twice the angle at the remaining part of the circle.
Asked by Samidhaindulkar133 | 11 Mar, 2021, 04:03: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×