Question:
Directions: How many total number of triangles are there in the problem figure given below ?
Directions: How many total number of triangles are there in the problem figure given below ?
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Name the vertices, list which pairs are joined by straight lines and count every set of three mutually joined, non-collinear points.
Updated On: Nov 12, 2026
- 11
- 12
- 10
- 9
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The Correct Option is B
Solution and Explanation
Let ABC be the large right triangle (A top, B bottom-left, C bottom-right). Let P be the inner point from which lines go to A, B and C. The horizontal line through P meets AB at L and the hypotenuse AC at M, and the vertical line from P meets AC at N (the order on AC is A, N, M, C).
Triangles containing P as a vertex:
with A: APL, APN, APM, APC, APB (5)
with B: BPL, BPC (2) (APB already counted)
with C: CPM, CPN (2) (APC, BPC already counted)
with M and N: PMN (1)
Triangles not containing P: ABC and ALM (2).
Total = 5 + 2 + 2 + 1 + 2 = 12.
Answer: (2) 12
Triangles containing P as a vertex:
with A: APL, APN, APM, APC, APB (5)
with B: BPL, BPC (2) (APB already counted)
with C: CPM, CPN (2) (APC, BPC already counted)
with M and N: PMN (1)
Triangles not containing P: ABC and ALM (2).
Total = 5 + 2 + 2 + 1 + 2 = 12.
Answer: (2) 12
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