Test
Triangle lines and circles
This test develops understanding of key triangle lines, including angle bisectors, medians and altitudes. It also covers incircles and circumcircles, their centres and related length calculations.
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Sample questions
- An angle bisector divides the opposite side into ___ cm and X cm. The adjacent sides are ___ cm and ___ cm. Find X.
- Find the midpoint of the segment with endpoints (___, ___) and (___, ___).
- A triangle has area ___ cm² and semiperimeter ___ cm. Find its inradius.
- The inradius is ___ cm and semiperimeter is ___ cm. Find the area.
- The sides are ___ cm, ___ cm and ___ cm, and area is ___ cm². Find the circumradius using S = abc/(4R).
Triangle lines and circles
The medians meet at the centroid, which divides every median in the ratio 2 : 1 from the vertex. Angle bisectors meet at the incentre, while perpendicular bisectors of sides meet at the circumcentre.
Altitudes and radii
The altitudes meet at the orthocentre. For the incircle, area A = rs where s is the semiperimeter; for the circumcircle, A = abc/(4R). Identify each centre from the defining lines rather than from its apparent position in a diagram.
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