Ask a Doubt
Request a call back

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

CBSE Class 11-science Answered

Let ABC be a triangle in which no angle is 90 . For any point P in the plane of the triangle, let E,F,G denotes reflection of P in the sides BC,CA,AB respectively . Prove the following statements: (a) If P is the incentre or an excentre of ABC , then P is the circumcentre of E,F,G; (b) If P is the circumcentre of ABC , then P is the orthocenter of E,F,G; (c) If P is the orthocenter of ABC , then P is either the incentre or an excentre of E,F,G.
Asked by | 01 Feb, 2012, 08:02: PM
answered-by-expert Expert Answer
Take the three sides to be AB as x - y + 1 =0 , AC as x + y - 1 =0 and BC as y = 0 ,
Then we can take any arbitrary point P one by one in all the four quadrants (a,b)(-a,-b)(a,-b)(-a,b)
For each point P find the reflections in AB BC CA , to get E F G .
Thus it becomes much simpler to prove for each case by calculating the othocenter , circumcenter and incenter of E F G   and then comparing with P
Answered by | 05 Feb, 2012, 08:13: AM

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 11-science - Maths
2 one
question image
Asked by dra | 24 Feb, 2024, 06:35: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
construction of Parabola When Distance between directrix and focus is given
Asked by praveenaditya843 | 22 Dec, 2023, 10:41: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
To construct Different types of conic sections
question image
Asked by praveenaditya843 | 21 Dec, 2023, 07:39: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
find the coordinates of the centre of a circle passing through the points(0,0),(-2,1)and(-3,2).also , find its radius .
question image
Asked by shakyajayprakash2006 | 08 Jun, 2022, 05:26: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Examine whether the point (4, 5) lies outside or inside the circle of equation x^2+y^2-2x-3=0
Asked by sbipo2000 | 23 Feb, 2020, 03:43: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
SIR PLEASE HELP ME WITH THIS QUESTIONS : 1. Find the equation of the tangent to the circle x^2+y^2=16 drawn from the point (1,4). 2. How many triangles can be formed by joining any 3 of the 9 points when i) no 3 of them  are collinear? ii) 5 of them are collinear? 3. AB is a line of fixed length, 6 units, joining the points A(t,0) and B which lies on thepositive y axis. P is a point on AB distant 2 units from A. Express the coordinates of B and P in terms of t. Find the locus of P as t varies. 4. In a triangle ABC, (b^2 - c^2) / (b^2 + c^2) = sin(B - C) / sin(B + C), prove that it is either a right-angled or isoceles triangle.
Asked by kandappan | 08 Feb, 2020, 11:29: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
6
question image
Asked by gauravmore604 | 04 Nov, 2019, 03:31: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
The locus of point for which sum of the squares of distances from cordinate axes is 25 is
Asked by Tejravi969 | 19 Aug, 2019, 06:08: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
Find the equation of the ellipse with centre at the origin , major axis on the x- axis and passing through the point (4,3) and (-1,4)..
Asked by Praktu111 | 09 Jun, 2019, 08:18: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 11-science - Maths
A stadium is in circular shape. Within the stadium some areas have been allotted for a hockey court and a javelin range, as given in the figure. Assume the shape of the hockey court and the javelin range to be square and triangle, resp. The curators would like to accommodate a few more sports in the stadium. Help them by measuring the unallocated region within the stadium.(the radius of the stadium is 200 mts.)  
Asked by rushabh1234 | 23 Jan, 2019, 08:59: 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
×