IMAT Mathematics: Part 3
An interactive quiz on Geometry and Measurement.
Fundamental Concepts Review
Trigonometry: Master SOH CAH TOA for right-angled triangles. For any triangle, use the Sine Rule $\frac{a}{\sin A} = \frac{b}{\sin B}$ and the Cosine Rule $c^2 = a^2+b^2-2ab\cos(C)$. The area can be found with $A = \frac{1}{2}ab\sin(C)$.
Circle Theorems: Key rules include the Tangent-Secant theorem ($PT^2 = PA \cdot PB$), properties of chords and radii, and relationships between angles (e.g., angle at the center is double the angle at the circumference).
Solid & Coordinate Geometry: Volume formulas for cones ($V=\frac{1}{3}\pi r^2h$) and other solids are essential. Use the distance and slope formulas to classify shapes on a coordinate plane.
Problem 10: Angle Bisector Length
HardIn triangle $\triangle ABC$, side $AB = 8$, side $BC = 10$, and angle $\angle ABC = 120^\circ$. A point D is on side AC such that BD bisects the angle $\angle ABC$. What is the length of the angle bisector BD?