In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio

In an equilateral triangle, the inradius, circumradius, and one of the exradii are in the ratio
A. `2: 4:5`
B. `1:2:3`
C. `1:2:4`
D. `2:4:3`

Monjur Alahi

5 views

2025-01-04 04:42

1 Answers

Salim Ahmed Kawsar

Correct Answer - B
We have
`Delta = (sqrt3)/(4) a^(2), s = (3a)/(2)`
`:. r = (Delta)/(s) = (a)/(2sqrt3), R = (abc)/(4Delta) = (a^(3))/(sqrt3 a^(2)) = (a)/(sqrt3)`
and `r_(1) = (Delta)/(s-a) = (sqrt3//4a^(2))/(a//2) = (sqrt3)/(2) a`
Hence, `r:R:r_(1) = (a)/(2sqrt3) :(a)/(sqrt3): (sqrt3)/(2) a = 1:2:3`

5 views Answered 2023-02-05 15:29

Related Questions

The distance between the two lines represented by the sides of an equilateral triangle a right-angled triangle an isosceles triangle none of these

2 Answers 5 Views

In triangle ABC, `R (b + c) = a sqrt(bc)`, where R is the circumradius of the triangle. Then the triangle is

2 Answers 8 Views

In triangle ABC, let `angle C = pi//2`. If r is the inradius and R is circumradius of the triangle, then `2(r + R)` is equal to

2 Answers 4 Views

If two sides of a triangle are roots of the equation `x^(2) -7x + 8 = 0` and the angle between these sides is `60^(@)` then the product of inradius an

2 Answers 5 Views

If in triangle `A B C ,sumsinA/2=6/5a n dsumI I_1=9` (where `I_1,I_2a n dI_3` are excenters and `I` is incenter, then circumradius `R` is equal to `(1

2 Answers 4 Views

If `R_(1)` is the circumradius of the pedal triangle of a given triangle ABC, and `R_(2)` is the circumradius of the pedal triangle of the pedal trian

2 Answers 5 Views

In `DeltaABC, R, r, r_(1), r_(2), r_(3)` denote the circumradius, inradius, the exradii opposite to the vertices A,B, C respectively. Given that `r_(1

2 Answers 5 Views

Circumradius of `DeltaABC` is 3 cm and its area is `6 cm^(2)`. If DEF is the triangle formed by feet of the perpendicular drawn from A,B and C on the

2 Answers 6 Views

Each side of an equilateral triand 12 is \( 24 cm \) the mid - point of its sides are joined to form another tranpla this brress is doins centinuously infinite 46. The perimeter of 7 th triangle is \( ( \) in \( cm ) \) a) \( \frac{3}{4} \) b) \( \frac{5}{8} \) c) \( \frac{9}{8} \) d) \( \frac{7}{8} \) 47. The sum of perimeter of all triangle is (in \( cm \) ) a) 144 b) 625 c) 400 d) 169 48. The area of all the triangle is (in sq cm) a) 576 b) \( 144 \sqrt{3} \) c) \( 169 \sqrt{3} \) d) \( 192 \sqrt{3} \) 49. The sum of perimeter of first 6 triangle is (in \( cm \) ) a) 120 b) \( \frac{567}{4} \) c) \( \frac{569}{4} \) d) 144 50. The side of the 5th triangle is (in \( cm \) ) a) 6 b) \( 1.5 \) c) \( 0.75 \) d) 3

2 Answers 5 Views

One side of an equilateral triangle is 36 cm. The mid-points of its sides are joined to form another triangle. Again another triangle is formed by joi

2 Answers 7 Views

এক্সাম দিয়ে মেধা যাচাই করুন

Job Preparation (1125)

Admission (754)

এসএসসি (10)

এইচএসসি (5)