Circles
Cyclic Quadrilaterals
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.</p><p><strong>Let FG and AH intersect at point K, then the length of AK =</strong></p>
<p>(a) \(\frac{192}{25}\)</p>
<p>(b) \(\frac{216}{25}\)</p>
<p>(c) \(\frac{225}{24}\)</p>
<p>(d) 9</p>
Step-by-Step Solution
Key Concept: Use properties of cyclic quadrilaterals and similar triangles to find the intersection point K.
<p>No solution provided in source material.</p>
Correct Answer: B