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CBSE Class 10 Answered

Show that the center of the incircle of a triangle is the point of intersection of the angle bisectors.
Asked by araima2001 | 03 Nov, 2015, 09:51: 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 f i g u r e.
L e t space O space b e space t h e space c e n t r e space o f space t h e space i n c i r c l e space a space t r i a n g l e. T h u s comma space O D space a n d space O E space b e space t h e space i n r a d i u s space o f space t h e space i n c i r c l e. rightwards double arrow O D equals O E C o n s i d e r space t h e space t r i a n g l e s comma space triangle B D O space a n d space triangle B E O B D space a n d space B E space a r e space t h e space tan g e n t s space t o space t h e space i n c i r c l e. A n d space h e n c e comma space angle B D O equals angle B E O equals 90 degree B O equals B O space open square brackets c o m m o n close square brackets S i n c e space tan g e n t s space f r o m space a space p o i n t space a r e space e q u a l comma space w e space h a v e comma space B D equals B F T h u s comma space b y space R H S space c o n g r u e n c e comma space w e space h a v e comma space triangle B D O asymptotically equal to triangle B E O T h e space c o r r e s p o n d i n g space p a r t s space o f space t h e space c o n g r u e n t space t r i a n g l e s space a r e space c o n g r u e n t. T h e r e f o r e comma space angle F B O equals angle O B D T h a t space i s space O B space i s space t h e space a n g l e space b i s e c t o r space o f space t h e space a n g l e space angle F B D. S i m i l a r l y space w e space c a n space p r o v e space t h a t comma space O A space i s space t h e space a n g l e space b i s e c t o r space o f space angle F A C A n d space O C space i s space t h e space a n g l e space b i s e c t o r space o f space t h e space a n g l e space angle A C B. T h u s space a l l space t h e space a n g l e space b i s e c o t r s space i n t e r s e c t space a t space t h e space p o i n t space O. T h a t space i s space t h e space a n g l e space b i s e c o t r s space i n t e r s e c t space a t space t h e space i n c e n t r e space o f space t h e space i n c i r c l e.
Answered by Vimala Ramamurthy | 04 Nov, 2015, 12:08: PM

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CBSE 10 - Maths
PQ is a chord of length 8 cm to a circle of radius 5 cm. The tangents P and Q intersect at a point T. Find the length of the tangent TP.
Asked by yalagondanikhil | 16 Apr, 2024, 12:25: PM
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CBSE 10 - Maths
in the given figure a triangle abc is drawn to circumscribe a circle of radius 3 cm such that the segment bd and dc are respectively of length 6 and 9 cm if the area of traingle abc is 54cm2 then find side ab and ac
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Asked by jennyy | 26 Mar, 2022, 08:41: PM
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CBSE 10 - Maths
3. Two supplementary angles are subtended at the centre by two arcs of a circle of radius 7 cm. Find the total length of these arcs  
Asked by sowmyashreeiyer | 31 Jan, 2022, 11:40: AM
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CBSE 10 - Maths
From a point P, two tangents PA and PB are drawn to a circle C(0, r).  If OP = 2r, then find ∠𝐴𝑃𝐵. What type of triangle is APB?  
Asked by riazu945 | 16 Jan, 2022, 01:00: PM
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CBSE 10 - Maths
in the above figure major
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Asked by ajabraosable27 | 11 Oct, 2021, 09:28: PM
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CBSE 10 - Maths
prime factorisation
Asked by amikasangma080 | 11 Oct, 2021, 06:14: PM
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CBSE 10 - Maths
prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact
Asked by muskanmahek2411 | 08 Oct, 2021, 10:48: PM
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CBSE 10 - Maths
radious of circle is
Asked by anishasheoran372 | 13 Jul, 2021, 09:33: AM
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CBSE 10 - Maths
In the adjoining figure, AB is the Diameter of the circle. E is not the centre. Angle ACD = 30°. Find angle x.
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Asked by bhilarevishwesh | 21 May, 2021, 08:27: AM
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CBSE 10 - Maths
Q30
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Asked by sangyaswarupa | 16 Mar, 2021, 10:06: AM
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