Geometryhard · Past Paper

A circle is inscribed in a triangle ABC with sides 8 cm, 10 cm, and 12 cm. Find the length of the segment of the side 12 cm from the vertex opposite to the side 10 cm.

A5 cm
B7 cm
C9 cm
D10 cm

✓ Correct Answer: A — 5 cm

Let tangent segments be x, y, z. x+y=8, y+z=10, z+x=12. 2(x+y+z)=30 => x+y+z=15. If side is 12 (x+z), then y=15-12=3. If side is 10(y+z), x=15-10=5.

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