Let ABCD be a cyclic quadrilateral. Prove that the orthocentres of the – InterviewSolution

InterviewSolution

1.	Let ABCD be a cyclic quadrilateral. Prove that the orthocentres of the triangles ABC, BCD, CDA, and DAB are the vertices of a quadrilateral congruent to ABCD. Also prove that the centroids of the triangles mentioned are the vertices of the cyclic quadrilateral.
Answer» Let ABCD be a cyclic quadrilateral. Prove that the orthocentres of the triangles ABC, BCD, CDA, and DAB are the vertices of a quadrilateral congruent to ABCD. Also prove that the centroids of the triangles mentioned are the vertices of the cyclic quadrilateral.

Discussion

No Comment Found

Related InterviewSolutions

Question 1 (ii)Can a polyhedron have for its faces:(ii) 4 triangles?
(i) Something happened at Lyonnesse. It was (a) improbable. (b) impossible. (c) unforeseeable. (ii) Pick out two lines from stanza 2 to justify your answer.
Take away: (i) 65x2−45x3+56+32x from x33−52x2+35x+14 (ii) 5a22+3a32+a3−65 from 13a3−34a2−52 (iii) 74x3+35x2+12x+92 from 72−x3−x25 (iv) y33+73y2+12y+12 from 13−53y2 (v) 23ac−57ab+23bc from 32ab−74ac−56bc
Question 5 Factorise: (i) 4x2+9y2+16z2+12xy−24yz−16xz(ii) 2x2+y2+8z2−2√2xy+4√2yz−8xz
What is the area of the red part as a fraction of the whole hexagon?
A figure has lines of symmetry as 4 and rotational symmetry of 2. Find its area given that its side length is 5m and base length is 6m and height is 4m .Find the area of the figure?
Question 4(iii)Numbers 1 to 10 is written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it.What is the probability of :getting a number greater than 6.
In the given figure, ABCD is a parallelogram. Find x.
Explain what is ψ and ψ^2.
In the graph given below,How many maximum values does y can have for one value of x?