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100+ Free PAU Technical Drawing II (Castilla y León) Practice Questions
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2026 Statistics
Key Facts: PAU Technical Drawing II (Castilla y León) Exam
90 min
Exam Duration
COPAU Castilla y León
0–10
Grading Scale (Min 4.0 for Access Phase)
Junta de Castilla y León
EUR 76.82
Base Registration Fee
Castilla y León PAU Fee Structure 2026
5 Core Blocks
Plane, Transformations, Dihedral, Axonometric, ISO Standards
2nd Bachillerato LOMLOE Curriculum
The Technical Drawing II exam for the Castilla y León PAU (Prueba de Acceso a la Universidad) features a 90-minute university entrance test administered by COPAU and the public universities of Castilla y León (USAL, UVA, UBU, ULE). Graded on a 0–10 scale, a minimum mark of 4.0 is required in the Access Phase to combine with Bachillerato GPA (60% Bachillerato + 40% PAU >= 5.0 to pass). The official exam consists of practical graphic drawing tasks; this dataset provides an English-language MCQ study adaptation designed for core concept practice, rule verification, and theoretical mastery.
Sample PAU Technical Drawing II (Castilla y León) Practice Questions
Try these sample questions to test your PAU Technical Drawing II (Castilla y León) exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1In plane geometry, what is the geometric relationship between a tangent line and the radius of a circle at the point of tangency?
A.They are parallel to each other.
B.They intersect at an angle of 45 degrees.
C.They are perpendicular to each other.
D.They intersect at an angle of 60 degrees.
Explanation: According to the fundamental properties of circle tangency, a line tangent to a circle is always perpendicular to the radius drawn to the point of tangency. This 90-degree angle relationship is essential for constructing tangents from external points or between circles.
2In any triangle, the center of the inscribed circle (incircle) is located at the intersection of which set of lines?
A.The three perpendicular bisectors of the sides
B.The three internal angle bisectors
C.The three altitudes from the vertices
D.The three medians connecting vertices to midpoints
Explanation: The incenter (incentro) of a triangle is the common point of intersection of its three internal angle bisectors. Because every point on an angle bisector is equidistant from the two adjacent sides, the incenter is equidistant from all three sides, making it the center of the inscribed circle.
3Which triangle center is formed by the intersection of the perpendicular bisectors (mediatrices) of its three sides?
A.Orthocenter
B.Incenter
C.Circumcenter
D.Centroid
Explanation: The circumcenter (circuncentro) is the point where the three perpendicular bisectors of the sides of a triangle intersect. It is equidistant from all three vertices of the triangle, serving as the center of the circumscribed circle.
4What is the name of the triangle center obtained by finding the intersection point of its three altitudes (alturas)?
A.Incenter
B.Orthocenter
C.Circumcenter
D.Excenter
Explanation: The orthocenter (ortocentro) is defined as the common point where the three altitudes (perpendicular lines dropped from each vertex to the opposite side or its extension) meet.
5The centroid (baricentro) divides each median of a triangle into two segments. What is the ratio of the distance from the vertex to the centroid compared to the distance from the centroid to the opposite side midpoint?
A.1 : 1
B.3 : 1
C.2 : 1
D.1 : 2
Explanation: The centroid divides each median in a 2:1 ratio. The segment from the vertex to the centroid is twice as long as the segment from the centroid to the midpoint of the opposite side.
6The golden ratio (sección áurea) divides a line segment AB at point C such that the ratio of the whole segment AB to the larger part AC equals what ratio?
A.The ratio of AC to the smaller part CB
B.The ratio of CB to the larger part AC
C.The ratio of AC to the sum AB + CB
D.The square of the ratio of AC to CB
Explanation: By definition, the golden section divides a segment AB at point C so that AB / AC = AC / CB = phi ≈ 1.618. The whole is to the greater part as the greater part is to the lesser part.
7For a point P located at distance d from the center of a circle O with radius R, what is the formula for the geometric power of point P (potencia de un punto) with respect to circle O?
A.K = d / R
B.K = d^2 + R^2
C.K = d^2 - R^2
D.K = (d - R)^2
Explanation: The power K of a point P relative to a circle with radius R and center O is defined as K = d^2 - R^2, where d = PO. When P is outside the circle, K is positive and equals the square of the length of the tangent segment drawn from P to the circle.
8What is the radical axis (eje radical) of two non-concentric circles?
A.The line segment connecting the centers of both circles
B.The locus of points having equal power with respect to both circles
C.The circle passing through the centers and intersection points of both circles
D.The perpendicular bisector of the line connecting their centers
Explanation: The radical axis of two circles is the locus of all points in the plane that have equal power with respect to both circles. It is always a straight line perpendicular to the line of centers.
9How is the radical center (centro radical) of three circles with non-collinear centers constructed geometrically?
A.As the midpoint of the triangle formed by the three centers
B.As the intersection of the three radical axes taken in pairs
C.As the center of the circumscribed circle passing through all three circle centers
D.As the average position of the three circle centers
Explanation: The radical center is the unique point in the plane having equal power with respect to three given circles. It is found by determining the radical axes of two pairs of circles; their intersection point is the radical center.
10For two mutually intersecting circles, where does their radical axis lie?
A.It is tangent to both circles at their highest points
B.It is the line passing through their two points of intersection
C.It is parallel to the line connecting their centers
D.It passes halfway between their centers regardless of radii
Explanation: When two circles intersect at two points, those intersection points have zero power with respect to both circles. Since zero power is equal power, the line passing through the two intersection points is the radical axis.
About the PAU Technical Drawing II (Castilla y León) Practice Questions
Verified exam format metadata for Castilla y León PAU Technical Drawing II (Dibujo Técnico II) Exam is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.