Grade 10 power mechanics – Tangency Quiz
1. In technical drawing for power mechanics, what is a tangent to a circle?
By definition, a tangent touches a circle at exactly one point and does not cross it; this is the property used in drawing tangents in power mechanics.
2. Which property is always true at the point where a radius meets a tangent to a circle?
A radius drawn to the point of tangency is perpendicular to the tangent line; this is a fundamental geometric property used in drawing and design.
3. How many tangents can be drawn from an external point to a circle?
From a point outside a circle you can draw two distinct tangent lines, each touching the circle at a different point.
4. When constructing a tangent from a point outside a circle using compass and straightedge, which step is essential?
The standard construction uses the line from external point to centre and constructs a right triangle (or uses the midpoint of that line) to locate the tangent points where the radius is perpendicular to the tangent.
5. What is a common external tangent to two circles?
An external common tangent touches both circles on their outer sides and does not intersect the segment joining the centres.
6. What is a common internal tangent to two circles?
An internal common tangent touches both circles and intersects the segment joining their centres; it lies between the circles.
7. If two circles are tangent externally, what is true about the distance between their centres?
When circles are externally tangent, the centres are separated by the sum of the radii because the circles touch at one point.
8. If two circles are tangent internally (one inside the other), the distance between their centres equals:
For internal tangency, the centre-to-centre distance equals the larger radius minus the smaller radius, since one circle lies inside the other touching at one point.
9. In belt drive drawings, the belt is tangent to pulleys. What point on a pulley is used to draw the tangent?
In belt drive drawings the belt touches the pulley at the contact point on the pulley circumference, which is the tangency point used to draw the belt path.
10. When two circles have equal radii, how many distinct common tangents do they have (if not overlapping)?
Two separate equal circles have four common tangents: two direct (external) and two transverse (internal) tangents, provided the circles do not overlap.
11. Which construction method is used to draw the common external tangents of two unequal circles in technical drawing?
A common method is to reduce the problem to tangents from a point by shrinking one circle by the other's radius (or vice versa), then drawing tangents to the reduced circle and transferring them back.
12. What happens to the tangent points when a line is tangent to two concentric circles (same centre)?
Concentric circles share a centre; no straight line can touch both at distinct single points without crossing between them, so common tangents do not exist.
13. When constructing a tangent from a point on the circumference of a circle, what is the correct direction of the tangent at that point?
At a point on the circumference the tangent is perpendicular to the radius drawn to that point; this determines the correct direction when drawing.
14. In technical drawings, the term 'point of contact' between a circle and a tangent refers to:
The point of contact (or point of tangency) is the unique point where the tangent line touches the circle.
15. For two non-overlapping circles, what is the easiest indicator that a straight line is an external common tangent?
An external common tangent does not cross the segment joining the centres; internal tangents do, so this tells them apart.
16. When drawing a tangent to a circle from a point on its circumference using a set square, which angle of the set square is used to ensure perpendicularity?
The tangent at a circumference point is perpendicular to the radius. Using the 90-degree corner of a set square ensures perpendicular construction.
17. In pulley layout for a flat belt, the belt segments between pulley contact points are approximated as:
Between pulleys the belt follows straight-line segments that are tangent to the pulley circumferences at contact points; drawings use these straight tangents.
18. Which statement about two tangent circles is correct when they touch externally at one point?
When two circles meet externally, they share the same tangent at the contact point because both radii to that point are collinear and perpendicular to the common tangent.
19. What is the general approach to construct a tangent to two unequal circles that are separated by a large distance (external tangents)?
You locate the homothetic centre along the line of centres and use the reduced circle (subtracting one radius) to find tangent directions; this is the standard geometric technique.
20. In a simple geometrical problem, the length of a tangent from an external point to a circle depends on:
Tangent length is found from right triangle formed by radius, tangent segment, and line from external point to centre, so it depends on that distance and radius.
21. Which is the correct relation for the tangent length t from external point P to circle centre O with radius r and OP = d?
Using the right triangle O, tangent point, and P, Pythagoras gives t^2 = d^2 - r^2, so t = sqrt(d^2 - r^2).
22. When two pulleys of different radii are connected by a belt, the belt wraps around each pulley at tangency points. If the pulleys are very close, what special case occurs?
When pulleys are close or arranged crossing, a crossed belt setup produces internal tangency segments (figure-eight); practical layouts must consider tangency geometry.
23. In drawing tangents to a circle using the compass method, why do we often draw an auxiliary circle or arc?
Auxiliary arcs or circles give construction points whose intersections determine exact tangent locations when using compass-and-straightedge methods.
24. Which of these is not true about tangent lines in technical drawing for power mechanics?
This is false: a tangent cannot be parallel to the radius at the point of contact because the radius is always perpendicular to the tangent there.
25. When designing a layout where a straight guide must touch two round shafts, which geometric construction is most useful?
To ensure the guide touches both shafts without interference, you must construct the appropriate common tangents so the line just contacts each shaft.
26. If a line is tangent to a circle at point T and you know the coordinates of the centre O and T, how can you find the tangent direction vector?
The tangent direction is perpendicular to the radius OT, so any vector perpendicular to OT gives the correct tangent direction.