If a, b, c are the sides of a right triangle where c is the hypotenuse then the radius r of the circle which touches the sides of the triangle is :

r = \frac{a + b + c}{2}

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r = \frac{b + c - a}{2}

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r = \frac{a + b - c}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

r = \frac{a + c - b}{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

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Solution

The correct option is A $r = \frac{a + b + c}{2}$
Let the circle touches sides AB,BC and CA at F,D and E respectively where AB=c,BS=a and AC=b

Length of the tangents drawn from an external point are equal.

$A E = A F$

$B D = B F$

$C E = C D = r$

$b - r = A F$

$a - r = B F$

So, $A B = A F + B F$

$c = b - r + a - r$

$c = a + b - 2 r$

$2 r = a + b - c$

$r = \frac{a + b - c}{2}$

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Similar questions

A, B and C are the sides of a right triangle where C is the hypotenuse. A circle of radius r touches the sides of the triangle prove that r is equal to $\frac{a + b - c}{2}$ .

Q. If a,b,c are the sides of a right triangle with c as the hypotenuse, prove that the radius r of the circle which touches the sides of the triangle is given by

r = \frac{a + b - c}{2}

Q. If a, b and c are the sides of a right angled triangle where c is the hypotenuse, then prove that the radius r of the circle which touches the sides of triangle is given by

r = \frac{a + b - c}{2}

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△ A B C, r_{A}, r_{B}, r_{C}

are the radii of the circles which touch the incircle and the sides emanating from the vertices

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Q. In triangle ABC,

∠ C = 90^{\circ} .

If inradius = r and circumradius = R, then find 2(r + R)?(a,b,c are the sides of the triangle opposite to angles A,B and C respectively)

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If a, b, c are the sides of a right triangle where c is the hypotenuse then the radius r of the circle which touches the sides of the triangle is :

The correct option is A r=a+b+c2Let the circle touches sides AB,BC and CA at F,D and E respectively where AB=c,BS=a and AC=bLength of the tangents drawn from an external point are equal.AE=AF BD=BFCE=CD=rb−r=AFa−r=BFSo, AB=AF+BFc=b−r+a−rc=a+b−2r2r=a+b−cr=a+b−c2