35 Year JEE Previous Questions: Properties of Triangle with solutions -

The sides of a triangle are 3x+4y, 4x+3y and 5x+5y where x, y > 0 then the triangle is

In a triangle with sides a, b, c, r₁ > r₂ > r₃ (which are the exradii) then

The sum of the radii of inscribed and circumscribed circles for an n sided regular polygon of  side a , is

In a triangle ABC, medians AD and BE are drawn. If AD = 4,   then the area of the Δ ABC is

If  in a ΔABC   then the sides a, b and c

The sides of a triangle are sin α, cos α and  Then the greatest angle of the triangle is

A person stan ding on t he bank of a river obser ves that  the angle of elevation of the top of a tree on the opposite bank of the river is 60° and when he retires 40 meters away from the tree the angle of elevation becomes 30°. The breadth of the river is

In a triangle ABC, let  If r is the inradius and R is the circumradius of the triangle ABC, then 2 (r + R) equals

If in a ΔABC , the altitudes from the vertices A, B, C on opposite sides are in H.P, then sin A, sin B, sin C are in

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of 60° at the foot of the tower, and the angle of elevation of the top of the tower from A or B is 30°.
The height of the tower is

AB is a vertical pole with B at the ground level and A at the top. A man finds that the angle of elevation of the point A from a certain point C on the ground is 60°. He moves away from the pole along the line BC to a point D such that CD = 7 m. From D the angle of elevation of the point A is 45°. Then the height of the pole is

For a regular polygon, let r and R be the radii of the inscribed and the circumscribed circles. A false statement among the following is

A bird is sitting on the top of a vertical pole 20 m high and its elevation from a point O on the ground is 45° . It flies off horizontally straight away from the point O. After one second, the elevation of the bird from O is reduced to 30° . Then the speed (in m/s) of the bird is

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are 30°, 45° and 60° respectively, then the ratio, AB : BC, is :