Question 17
Use support lines in Fig. 6.11 to construct a pointed arch. Make different arches, by changing the radius of the arcs.
- A pointed arch (Gothic arch) is constructed using two circular arcs drawn from two distinct center points on support lines.
- By keeping the compass radius identical for both centers, the arcs meet symmetrically at a top vertex or peak.
- Changing the radius creates different arch profiles — varying its sharpness, height, and width.
Step 1 · Identify Arc Centers
Let the intersection of the support lines be . Mark the two points on the support lines as on the left and on the right. Points and serve as the centers for the arcs.
Step 2 · Draw Intersecting Arcs
- Choose a compass radius long enough so that arcs drawn from and will intersect.
- With point as center and radius , draw an arc curving upward.
- With point as center and the same radius , draw an arc curving upward to intersect the first arc.
Step 3 · Form the Pointed Arch
Label the intersection point of the two arcs as .
The combined curves from to and to form the pointed arch with peak .
Step 4 · Vary the Radius to Create Different Arches
Repeat the construction using different radii :
- Smaller radius: Produces a taller, narrower, and sharper pointed arch.
- Larger radius: Produces a wider, flatter, and more rounded arch.
Construct the arch by drawing two intersecting arcs of equal radius with centers at and . Varying the radius creates arches of different heights and widths.
- Unequal Radii: Changing the compass width between drawing the arc from and the arc from makes the arch asymmetrical.
- Radius Too Small: If the radius is less than half the distance between and , the two arcs will not intersect at all.
More questions in FIO
When constructing the perpendicular bisector, is it necessary to have the same radius for the arcs above and below ? Explore this through construction, and then justify your answer.
[Hint 1: Any point that is of the same distance from and lies on the perpendicular bisector.
Hint 2: We can draw the whole line if any two of its points are known.]
Is it necessary to construct the pairs of arcs above and below ? Instead, can we construct both the pairs of arcs on the same side of ? Explore this through construction, and then justify your answer.
While constructing one pair of intersecting arcs, is it necessary that we use the same radii for both of them ? Explore this through construction, and then justify your answer.
Recreate this design using only a ruler and compass —
Justify why in Fig. 6.4 is the perpendicular bisector.
Can you think of different methods to construct a angle at a given point on a line using a rope?
Construct at least 4 different angles. Draw their bisectors.
Construct the 8-petalled figure shown in Fig. 6.5.
In Step 2 of angle bisection, if arcs of equal radius are drawn on the other side, as shown in the figure, will the line still be an angle bisector? Explore this through construction, and then justify your answer.
What are the other angles that can be constructed using angle bisection? Can you construct angle?
Come up with a method to construct the angle bisector using a rope.
Construct the following figure.
How do we construct the petals so that they are of the maximum possible size within a given square?
Construct at least 4 different angles in different orientations without taking any measurement. Make a copy of all these angles.
Construct the Fig. 6.6.
Construct 4 pairs of parallel lines in different orientations.
Construct the following figure.
Use support lines in Fig. 6.11 to construct a pointed arch. Make different arches, by changing the radius of the arcs.
Make your own arch designs.
Construct the following figures:
Optical Illusion: Do you notice anything interesting about the following figure? How does this happen? Recreate this in your notebook.
Construct this figure.
[Hint: Find the angles in this figure.]
Draw a line and mark a point anywhere outside the line. Construct a perpendicular to the given line through .
[Hint: Find a line segment on whose perpendicular bisector passes through .]
How can the tangram pieces be rearranged to form each of the following figures?
Are the following tilings possible?