Geometry
Plane Euclidean geometry — triangles, circles, transformations and coordinate methods.
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Take a full mock →Q1 · Geometry · MEDIUM
In triangle ABC, the medians from vertices A and B are perpendicular to each other. If AB = 12 cm, what is the length of the median from vertex C (in cm)?
Q2 · Geometry · HARD
A circle is inscribed in a triangle with sides 13, 14, and 15. What is the radius of the inscribed circle?
Q3 · Geometry · HARD
In triangle ABC, ∠BAC = 60°. The angle bisectors of ∠ABC and ∠ACB meet at I. If the perpendicular distance from I to BC is 8 units and the inradius is r, find the value of r.
Q4 · Geometry · MEDIUM
A circle with center O has radius 10 cm. Two chords AB and CD intersect at point P inside the circle such that AP = 8 cm, PB = 6 cm, and CP = 12 cm. Find the length of PD in cm.
Q5 · Geometry · EASY
In triangle ABC, the perpendicular from A to BC meets BC at D. If BD = 9, DC = 16, and AD = 12, find the area of triangle ABC.