Choose the correct statement(s) from the options:
1. The construction method to prove similarity of the constructed triangles is proved by the AA similarity method.
In the above diagram, ΔA′BC′ has been constructed that is similar to ΔABC. A'C' has been constructed parallel to AC. Hence, the similarity of the triangles can be proved by the AA similarity method.
2. Proof : For a tangent, the perpendicular line from the point of contact to the circle passes through the centre.
Let O be the centre of the given circle.
AB is the tangent drawn touching the circle at A.
Draw AC ⊥ AB at point A, such that point C lies on the given circle.
∠OAB = 90° (Radius of the circle is perpendicular to the tangent)
Given ∠CAB = 90°
∴ ∠OAB = ∠CAB
This is possible only when centre O lies on the line AC.
Hence, perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.
3. The ratio of division must always be positive and rational. It can be greater than or less than 1.
4. Similarity of triangles is the basic principle used in dividing a line segment.
In this case, Similar triangles ACA3 and ABA5 have been constructed to divide the line segment AB.