Concurrent Lines
NIOS · Class 10 · Maths
Flashcards for Concurrent Lines — NIOS Class 10 Maths. Quick Q&A cards covering key concepts, definitions, and formulas.
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See them allIn triangle ABC, if the angle bisectors AD, BE, and CF meet at point I, find the inradius if the sides are 3 cm, 4 cm, and 5 cm.
Answer
Step 1: Check if it's a right triangle: 3² + 4² = 9 + 16 = 25 = 5². Yes, it's a right triangle. Step 2: For a right triangle with legs a, b and hypotenuse c, inradius r = (a + b - c)/2 Step 3: r = (3 …
Find the circumradius of an equilateral triangle with side length 6 cm.
Answer
Step 1: For an equilateral triangle, circumradius R = a/√3 where a is the side length Step 2: R = 6/√3 = 6/√3 × √3/√3 = 6√3/3 = 2√3 cm Step 3: Alternative method using altitude: altitude h = (√3/2) × …
In triangle ABC, G is the centroid and AG = 8 cm. Find the length of the median AD.
Answer
Step 1: Recall that centroid divides each median in the ratio 2:1 Step 2: AG:GD = 2:1, which means AG = (2/3) × AD Step 3: Given AG = 8 cm, so 8 = (2/3) × AD Step 4: AD = 8 × (3/2) = 12 cm Step 5: Ver…
Prove that in an isosceles triangle ABC where AB = AC, the angle bisector from A is also the perpendicular bisector of BC.
Answer
Step 1: Let AD be the angle bisector of ∠BAC, meeting BC at D Step 2: In triangles ABD and ACD: - AB = AC (given) - ∠BAD = ∠CAD (AD bisects ∠A) - AD = AD (common side) Step 3: By SAS congruence, △ABD …
When do you use the formula for circumradius R = abc/(4K) where K is the area?
Answer
Use this formula when: 1. You know all three sides (a, b, c) of the triangle 2. You can calculate the area using Heron's formula or other methods 3. You need to find circumradius for any triangle type…
Find the coordinates of the centroid of triangle with vertices A(2,3), B(4,7), and C(6,1).
Answer
Step 1: Centroid formula: G = ((x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3) Step 2: Identify coordinates: A(2,3), B(4,7), C(6,1) Step 3: x-coordinate of centroid = (2+4+6)/3 = 12/3 = 4 Step 4: y-coordinate of centroid…
In triangle ABC, the altitudes are AD, BE, and CF. If triangle is obtuse at B, where is the orthocentre located?
Answer
Step 1: For an obtuse triangle, the orthocentre lies outside the triangle Step 2: Since ∠B is obtuse (>90°), the orthocentre H lies on the opposite side of BC from vertex A Step 3: To locate H: - Exte…
Solve: Find the inradius of triangle with sides 8, 15, and 17 units.
Answer
Step 1: Check triangle type: 8² + 15² = 64 + 225 = 289 = 17². It's a right triangle. Step 2: For right triangle with legs a, b and hypotenuse c: r = (a + b - c)/2 Step 3: r = (8 + 15 - 17)/2 = 6/2 = 3…
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