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In a right-angled isosceles triangle, th...

In a right-angled isosceles triangle, the ratio of the circumradius and inradius is

A

`2(sqrt2 + 1) : 1`

B

`(sqrt2 + 1): 1`

C

`2 : 1`

D

`sqrt2 : 1`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `R = (sqrt2a)/(2) = (a)/(sqrt2)`
`r = (Delta)/(s) = ((1)/(2)a^(2))/((1)/(2) (a + a + sqrt2a)) = (a)/(2+ sqrt2)`
`:. (R)/(r) = (a)/(sqrt2) xx (2 + sqrt2)/(a) = sqrt2 + 1`
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CENGAGE ENGLISH-PROPERTIES AND SOLUTIONS OF TRIANGLE-Exercises
  1. In Delta ABC, "cot"(A)/(2) + "cot" (B)/(2) + "cot" (C)/(2) is equal to

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  2. In A B C ,(cot (A/2)+cot(B/2))(asin^2(B/2)+bsin^2(A/2))= (a) cotC (...

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  3. In a right-angled isosceles triangle, the ratio of the circumradius an...

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  4. In a ΔABC, a semicircle is inscribed, whose diameter lies on the side ...

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  5. In DeltaABC, A = (2pi)/(3), b -c = 3 sqrt3 cm and " area of " Delta AB...

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  6. In triangle ABC, let angle C = pi//2. If r is the inradius and R is ci...

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  7. In the given figure, AB is the diameter of the circle, centered at O. ...

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  8. In triangle A B C ,ifPdotQ ,R divides sidesB C ,A C , and A B , respec...

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  9. If the angles of a triangle are 30^(@) and 45^(@), and the included si...

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  10. In triangle A B C , base B C and area of triangle are fixed. The locus...

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  11. let the area of triangle A B C be ((sqrt(3)-1))/2,b=2 , and c=(sqrt(3)...

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  12. In DeltaABC, Delta = 6, abc = 60, r=1. Then the value of (1)/(a) + (1)...

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  13. Triangle ABC is isosceles with AB=AC and BC=65cm. P is a point on BC s...

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  14. In an equilateral triangle, the inradius, circumradius, and one of the...

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  15. In triangle ABC, if cos A + cos B + cos C = (7)/(4), " then " (R)/(r) ...

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  16. If two sides of a triangle are roots of the equation x^(2) -7x + 8 = 0...

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  17. Given b = 2, c = sqrt3, angle A = 30^(@), then inradius of DeltaABC is

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  18. In triangle ABC, if A - B = 120^(2) and R = 8r, where R and r have the...

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  19. A B C is an equilateral triangle of side 4c mdot If R ,r and h are the...

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  20. A circle is inscribed in a triangle A B C touching the side A B at D s...

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