A Coefficient Decomposition

★ 7/10trigonometry Law of Cosines Triangle Geometry vectors

Problem

In $\triangle ABC$ , the sides opposite $A, B, C$ are $a, b, c$ . A point $M$ lies on side $AB$ , and a point $P$ on line $CM$ satisfies

\overrightarrow{CP} = \frac{\overrightarrow{CA}}{b\cos A} + \frac{\overrightarrow{CB}}{a\cos B}.

Given $\left|\overrightarrow{CM}\right| = \dfrac{c}{2}$ and $a^2 + b^2 = 2\sqrt{2}ab$ , find $C$ .

Answer

Solution

Difficulty	7/10
Topics	trigonometry, Law of Cosines, Triangle Geometry, vectors

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.