Problem
GEO-B1-M03-P010 Altitude to the Hypotenuse
#10
★★☆☆☆ Level 2 of 5
In right triangle \(ABC\), angle \(C\) is right, and \(CH\) is the altitude to hypotenuse \(AB\). It is known that \(AH=3\), \(HB=12\). Find \(CH\).
Use similarity of the small right triangles: \(CH^2=AH\cdot HB\).
From the similarity of triangles \(ACH\) and \(CBH\), \(\frac{CH}{AH}=\frac{HB}{CH}\). Therefore \(CH^2=AH\cdot HB=3\cdot12=36\), so \(CH=6\).
It is better to derive the formula through similarity, not give it as memorised.