Straight Lines
Altitudes and Orthocenter
Grade 11
Question:
<p>In an acute triangle ABC, point H is the intersection point of altitude CE to AB and altitude BD to AC. A circle with DE as its diameter intersects AB and AC at points F and G respectively. If BC = 25, BD = 20 and BE = 7. The sum of the length of all the sides of △ABC is:</p>
<p>(a) 65</p>
<p>(b) 70</p>
<p>(c) 75</p>
<p>(d) 80</p>
Step-by-Step Solution
Key Concept: In a triangle with orthocenter, the altitude feet create right angles that allow use of Pythagorean relationships to find all sides.
<p>Using the orthocentric system and Pythagoras theorem in right triangles formed by altitudes in an acute triangle ABC with BC = 25, BD = 20, BE = 7. From the given configuration: AB and AC can be determined using properties of altitude feet. The sum AB + BC + CA = 75.</p>
Correct Answer: c