Consider the trapezoid ABCD where A = (0,0), B = (9,0), C = (8,4) and D = (5,4). The diagonals of this trapezoid intersect at point Q. (a) Draw a sketch of this trapezoid. (b) Find the coordinates of Q. (c) Which two triangles inside the trapezoid are similar
Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
- Consider the trapezoid ABCD where A = (0,0), B = (9,0), C = (8,4) and D = (5,4). The diagonals of this trapezoid intersect at point Q.
- (a) Draw a sketch of this trapezoid.
- (b) Find the coordinates of Q.
- (c) Which two
triangles inside the trapezoid are similar - (d) What is the ratio of the areas of the similar triangles you found in part (c)?
- (e) Find the areas of ∆ADQ and ∆BCQ.
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