Problem 1 :
Prove by vector method that if a line is drawn from the center of the circle to the midpoints of a chord, then the line is perpendicular to the chord.
Solution :
Let C be the midpoint of the chord AB. O is the center of circle.
OA = OB = radius.
So, OC is perpendicular to AB.
Problem 2 :
Prove by vector method that the median to the base of an isosceles triangle is perpendicular to the base.
Solution :
Since OC is the median AC = AB. The above triangle is isosceles triangle of equal sides OA and OB.
Then base of an isosceles triangle is perpendicular to its median.
Problem 3 :
Prove by vector method that an angle in a semicircle is a right angle.
Solution :
Angle in a semicircle is right angle.
Problem 4 :
Prove by vector method that the diagonals of a rhombus bisect each other at right angles.
Solution :
In rhombus, all the sides will be equal.
Problem 5 :
Using vector method, prove that if the diagonals of a parallelogram are equal, then it is a rectangle.
Solution :
AB is perpendicular to AC, then it is rectangle.
Problem 6 :
Prove by vector method that the area of the quadrilateral ABCD having diagonals AC and BD is
Solution :
Area of quadrilateral ABCD
= Area of triangle ABC + area of ADC
Problem 7 :
Prove by vector method that the parallelogram on the same base between the same parallels are equal in area.
Solution :
Problem 8 :
If G is the centroid of a triangle ABC, prove that
Area of triangle GAB = area of triangle GBC = area of triangle GCA = 1/3 area of triangle ABC
Solution :
G is the centroid and it is dividing AG to GD in the ratio 2 : 1.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM