Question

in a triangle ABC, AB=8cm angle abc is equals to 90degree then find the radius of the circle inscribed in the triangle​

Answer 1

Answer:

were is the image bro

Answer 2

Step-by-step explanation:

Given : In a right triangle abc, AB = 8 cm and AC = 6 cm. Find the radius of its in-circle.

To find : Radius of the circle inscribed in the triangle.

Solution :

AB = 8 cm ; AC = 6 cm.

By applying Pythagoras theorem,

BC² = AB² + AC²

BC² = 8² + 6²

= 64 + 36

BC² = 100

BC = 10 cm.

Formula :

Radius of triangle = \frac{\text { Area of triangle }}{\text { Semi-perimeter of triangle }}

Semi-perimeter of triangle

Area of triangle

Area of triangle = \frac{1}{2}\times\{b\}\times\{h\}

2

1

×{b}×{h}

Semi-perimeter of triangle = \frac{a+b+c}{2}

2

a+b+c

Finding radius of the circle inscribed in the triangle :

Area of triangle = \frac{1}{2}\times\{b\}\times\{h\}

2

1

×{b}×{h}

= \frac{1}{2}\times\{6\}\times\{8\}

2

1

×{6}×{8}

= \frac{1}{2}\times\{48\}

2

1

×{48}

Area of triangle = 24

Semi-perimeter of triangle = \frac{a+b+c}{2}

2

a+b+c

a = 8 ; b = 6 ; c = 10

= \frac{8+6+10}{2}

2

8+6+10

= \frac{24}{2}

2

24

Semi-perimeter of triangle = 12.

Radius of triangle = \frac{\text { Area of triangle }}{\text { Semi-perimeter of triangle }}

Semi-perimeter of triangle

Area of triangle

= \frac{24}{12}

12

24

Radius of triangle = 2 cm.

Therefore, the radius of the circle inscribed in the triangle is 2 cm.