Mathematics - Properties of Triangle Question with Solution | TestHub
MathematicsProperties of TriangleMiscellaneous/Mixed (Include Hight & Distance)Medium2 minQB
MathematicsMediuminteger
Passage / Comprehension
In an acute ΔABC , point H is the point of intersection of altitudes CE, BD and AP to sides AB, AC and BC respectively. A circle with DE as its diameter intersects AB and AC at the points F and G respectively. FG and AH intersects at point K. If BC = 25, BD = 20, BE = 7, then (D,E,P lie on AC, AB, BC respectively)
If the length of the segment AK is k, then [k] is equal to (where [.] denotes the greatest integer function)
Answer:
8
Solution:
From BE = 7, BC = 25: cos B = 7/25, sin B = 24/25. From BD = 20, BC =25: sin C = 4/5. Hence AB = 25, AC = 30. Take . , . Circle on diameter DE meets AB at and AC at . So FG is . AH is the altitude from A: x = 7. So and , therefore .
Stream:JEESubject:MathematicsTopic:Properties of TriangleSubtopic:Miscellaneous/Mixed (Include Hight & Distance)
⏱ 2mℹ️ Source: QB
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