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100+ Free Canary Islands PAU Technical Drawing II Practice Questions
Canary Islands PAU Technical Drawing II (Dibujo Técnico II 2º Bachillerato COPAU 2026) practice questions are available now; exam metadata is being verified.
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Sample Canary Islands PAU Technical Drawing II Practice Questions
Try these sample questions to test your Canary Islands PAU Technical Drawing II exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1At which notable point of a triangle do the three perpendicular bisectors of its sides converge, and what is its fundamental geometric property?
A.Centroid (barycenter); it represents the center of mass of the triangle.
B.Circumcenter; it is the center of the circle circumscribed about the triangle.
C.Orthocenter; it is the point of intersection of the three altitudes.
D.Incenter; it is the center of the circle inscribed in the triangle.
Explanation: The circumcenter is the point where the three perpendicular bisectors of a triangle intersect. Since the perpendicular bisectors are the loci of points equidistant from the endpoints of each side, the circumcenter is equidistant from the three vertices, making it the center of the circumscribed circle.
2The centroid G of a triangle divides each of its medians into two segments. What is the ratio of the distance between the centroid and the midpoint of the opposite side to the median's total length?
A.It corresponds to 1/4 of the median's total length.
B.It corresponds to 1/2 of the median's total length.
C.It corresponds to 1/3 of the median's total length.
D.It corresponds to 2/3 of the median's total length.
Explanation: The centroid G divides each median in a 2:1 ratio, counted from the vertex. Therefore, the distance from the centroid to the midpoint of the opposite side is exactly 1/3 of the median's total length, while the distance to the vertex is 2/3.
3In a non-equilateral triangle, the Euler line contains three of its notable points. Which set of notable points must necessarily lie on the Euler line?
A.Circumcenter, Centroid, and Orthocenter.
B.Incenter, Circumcenter, and Centroid.
C.Incenter, Centroid, and Orthocenter.
D.Circumcenter, Incenter, and Orthocenter.
Explanation: The Euler line of any non-equilateral triangle passes through the circumcenter (O), the centroid (G), and the orthocenter (H). Furthermore, the vector relation GH = 2 · OG holds. The incenter belongs to this line only in isosceles triangles.
4The nine-point (Feuerbach) circle of a triangle passes through nine of its notable points. Which of the following statements about its radius is correct?
A.Its radius equals twice the radius of the circumscribed circle.
B.Its radius equals the radius of the inscribed circle.
C.Its radius is exactly half the radius of the circumscribed circle.
D.Its radius equals 1/3 of the sum of the triangle's three altitudes.
Explanation: The radius of the nine-point (Feuerbach) circle ($R_N$) equals half the radius of the circle circumscribed about the triangle ($R_N = R/2$). Its center is the midpoint of the segment joining the circumcenter and the orthocenter.
5To construct a triangle knowing side a, the altitude $h_a$, and the opposite angle $∠A$, which locus must be drawn relative to the given segment a?
A.The perpendicular bisector of a and a concentric circle.
B.The bisectors of angle $∠A$ applied at the endpoints of a.
C.A homothety of segment a with ratio $h_a$.
D.The inscribed-angle locus (arc) subtending angle $∠A$ over segment a, together with the lines parallel to a at distance $h_a$.
Explanation: Vertex A must simultaneously belong to the inscribed-angle locus (arc) that subtends angle $∠A$ over segment a (the locus of points from which a is seen at angle $∠A$) and to the line parallel to a located at distance $h_a$. The intersection of both figures determines the position of A.
6Which notable center of a triangle is obtained by drawing the bisectors of its three interior angles?
A.The orthocenter.
B.The circumcenter.
C.The incenter.
D.The main excenter.
Explanation: The incenter is the point where the bisectors of the triangle's three interior angles meet. It is the center of the inscribed circle, which is tangent to the triangle's three sides.
7In the golden section of a segment of length L, the larger segment x satisfies the relation $x^2 = L · (L - x)$. What is the approximate numerical value of the larger golden ratio $Φ = x / (L - x)$?
A.1.414
B.1.618
C.1.732
D.2.618
Explanation: The golden ratio $Φ = (1 + √5) / 2 ≈ 1.618033...$ represents the proportion between the larger and smaller sections of a segment divided in golden section.
8What geometric relationship exists between the length of side $d_{10}$ of a regular decagon inscribed in a circle of radius R and that radius R?
A.Side $d_{10}$ is the golden section of radius R.
B.Side $d_{10}$ equals radius R multiplied by $√(3)$.
C.Side $d_{10}$ is the harmonic mean between R and the side of the hexagon.
D.Side $d_{10}$ is exactly half the radius ($R/2$).
Explanation: In a regular decagon inscribed in a circle of radius R, side $d_{10} = R · (√5 - 1) / 2$, which coincides exactly with the larger golden section of radius R.
9When constructing a regular pentagon inscribed in a circle of radius R using the classical method, the decagon side $d_{10}$ and the hexagon side $l_6 = R$ are obtained first. How is the length of the pentagon side $l_5$ obtained numerically and graphically?
A.It is the geometric mean between radius R and the decagon side $d_{10}$.
B.It is the sum of the sides $l_6 + d_{10}$.
C.It is the difference between the sides $l_6 - d_{10}$.
D.It is the hypotenuse of a right triangle whose legs are $l_6 = R$ and the decagon side $d_{10}$.
Explanation: In the right triangle formed in the classical Richmond/Ptolemy construction, the legs measure $R$ (hexagon side $l_6$) and $d_{10}$ (decagon side). By the Pythagorean theorem, the hypotenuse is $l_5 = √(R^2 + d_{10}^2)$.
10How many distinct regular star polygons with 7 vertices (star heptagons) can be constructed?
A.None, because 7 is a prime number.
B.Three, with steps 2, 3, and 4.
C.Two, with steps 2 and 3.
D.Only one, with step 2.
Explanation: The valid steps p for a star polygon with N vertices must satisfy $1 < p < N/2$ and be coprime with N. For N = 7, $N/2 = 3.5$, so the valid integer steps are $p = 2$ and $p = 3$. Therefore, there are 2 distinct star heptagons.
About the Canary Islands PAU Technical Drawing II Practice Questions
Verified exam format metadata for Canary Islands PAU Technical Drawing II (Dibujo Técnico II 2º Bachillerato COPAU 2026) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.