Geometry Answers

A triangle is placed in a semicircle with a radius of 2mm what is the area of the shaded region use the value 3.14 and do not round the number

ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD.

In a quadrilateral OABC, D is the midpoint of BC and E is the point on AB such that AE:ED=2:1 , given that OA=a, OB=b and OC=c express OD and OE in terms of a,b and c

Show that the points P(–5, 0), Q(–2, 3), and R(6, –11) lie on a circle with its center at C(2, 4). Conclude by explaining why your findings show this. 

The points D, E and F divide the sides BC, CA and AB of a triangle in the ratio 1:4, 3:2 and 3:7 respectively. Show that there exists a point G such that the sum of the vectors AD, BE, CF is parallel to CG. What is the ratio in which G divides AB?

1. In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such

that AE : ED = 2 : 1. Given that OA = a, OB = b and OC = c, express OD and

OE in terms of a, b and c.

In a quadrilateral OABC, D is the midpoint of BC and E is the point on AD such that AE : ED = 2 : 1. Given that OA = A, OB = B, and OC = c express OD and OE in terms of a,b and c.

ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x

and AC = 2y, express the vectors (i) BC, (ii) PQ, (iii) PC, (iv) BQ in terms of x

and y. What can you deduce about the directed line-segments BC and PQ?

Let BCB′C′ be a rectangle, let M be the midpoint of B′C′, and let A be a point on the circumcircle of the rectangle. Let triangle ABC have orthocenter H, and let T be the foot of the perpendicular from H to line AM. Suppose that AM= 2, [ABC] = 2020, and BC= 10. Then AT=m/n, where m and n are positive integers with gcd (m,n) = 1. Compute 100m+n.

The area of a triangle is 72, and one side is 24. If the corresponding side

in a similar triangle is 16, find its area.