NDA || Mathematics || Geometry || Quiz 2020

In ∆ABC, ∠C = 90^o and D is a point on CB such that AD is the bisector of ∠A. If AC = 10 cm and BC = 24 cm, then what is the length of AD?

An equilateral triangle has one vertex at (0, 0) and another at  What are the coordinates of the third vertex?

Three straight lines are drawn through the three vertices of a triangle ABC, the line through each vertex being parallel to the opposite side. The triangle DEF is bounded by these parallel lines. Consider the following statements in respect of the triangle DEF:

1) Each side of triangle DEF is double the side of triangle ABC to which it is parallel

2) Area of triangle DEF is four times the area of triangle ABC

Which of the above statements is/are correct?

In a triangle ABC, AD is the median through A and E is the midpoint of AD, and BE produced meets AC at F. Then AF is equal to

A railroad curve is to be laid on a circle. What radius (approximate) should be used if the track is to change direction by 25^o in a distance of 120 m?

If every side of an equilateral triangle is doubled, then the area of new triangle becomes k times the area of the old one. What is k equal to?

In a triangle ABC, AD is perpendicular to BC and BE is perpendicular to AC. Which one of the following is correct?

ABC is triangle right-angled at B. if AB = 6 cm and BC = 8 cm, then what is the length of the circum-radius of the triangle ABC?

Let ABC be a triangle in which ABC = 60^o and AC = x < BC. Let the circle with centre at C and radius x meet BC at D. Let CF be the perpendicular drawn from C meeting AD at F.

Statement-I: Triangle ACD is isosceles but not equilateral

Statement-II: DF = x/2

Which one of the following is correct in respect of the above statements?

A rectangle of maximum area is drawn inside a circle of diameter 5 cm. what is the maximum area of such a rectangle?