Properties of Triangle
Showing 26 of 26 · 26 total
- 1.If two vertices of an equilateral triangle are A(-a,0) and B(a,0), a>0, and the third vert…Medium
- 2.In a triangle with sides a, b, c, r_1 > r_2 > r_3 (which are the ex-radii) then :Easy
- 3.The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon…Medium
- 4.In a triangle ABC, medians AD and BE are drawn.Medium
- 5.If in a [ ABC] [a, ^2( C 2 ) + c, ^2( A 2 ) = 3b 2,] then the sides a, b and c :Medium
- 6.The sides of a triangle are [ ,, ] and [ 1 + ] for some [0 < < 2].Medium
- 7.If in a [ ABC], the altitudes from the vertices A, B, C on opposite sides are in H.P, then…Medium
- 8.In a triangle ABC, let [ C = 2].Medium
- 9.For a regular polygon, let r and R be the radii of the inscribed and the circumscribed cir…Medium
- 10.In a [ PQR, 1mu 1mu 1mu ] If [3 1mu 1mu P + 4 1mu 1mu Q = 6] and [4 Q + 3 P = 1,] then the…Medium
- 11.The angles A, B and C of a triangle ABC are in A.P.Medium
- 12.With the usual notation, in [ ]ABC, if [ A + B] = 120o, a = [ 3 ] + 1, b = [ 3 ] - 1 then …Medium
- 13.Given [b + c 11 = c + a 12 = a + b 13] for a [ ]ABC with usual notation.Medium
- 14.In a triangle, the sum of lengths of two sides is x and the product of the lengths of the …Medium
- 15.If the lengths of the sides of a triangle are in A.P.Hard
- 16.If in a triangle ABC, AB = 5 units, [ B = ^ - 1( 3 5 )] and radius of circumcircle of []AB…Medium
- 17.Let a, b, c be in arithmetic progression.Medium
- 18.The triangle of maximum area that can be inscribed in a given circle of radius 'r' is :Medium
- 19.Let [ A B = (A - C) (C - B)], where A, B, C are angles of triangle ABC.Medium
- 20.Let a, b and c be the length of sides of a triangle ABC such that [a + b 7 = b + c 8 = c +…Medium
- 21.The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 - 2x2.Medium
- 22.In a triangle ABC, if [ A+2 B+ C=2] and the lengths of the sides opposite to the angles A …Medium
- 23.For a triangle ABC, the value of [ 2A + 2B + 2C] is least.Medium
- 24.Let [(5, (a)/(4))] be the circumcenter of a triangle with vertices [A(a,-2), B(a, 6)] and …Medium
- 25.Two vertices of a triangle [ABC] are [A(3,-1)] and [B(-2,3)], and its orthocentre is [P(1,…Hard
- 26.Let the area of a P Q R with vertices P(5,4), Q(-2,4) and R(a, b) be 35 square units.Medium