In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively, let D be a point on the line segment BC such that AD is perpendicular to BC. If AD=3 cm then what is the radius in cm of the circle circum scribing the triangle ABC?Choices:- 17.05 27.85 22.45 26.25

To solve this problem, we need to use the formula for the radius (R) of the circumcircle of a triangle, which is given by:

R = abc/4K

where a, b, and c are the sides of the triangle and K is the area of the triangle.

First, we need to find the length of the side BC. Since AD is perpendicular to BC, we can use the Pythagorean theorem to find BC. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. So, we have:

(AB)^2 = (AD)^2 + (BD)^2 (17.5)^2 = (3)^2 + (BD)^2 BD = sqrt((17.5)^2 - (3)^2) = 17.25 cm

Since AD is perpendicular to BC, triangle ABD is a right triangle. Therefore, triangle ABC is an isosceles triangle, and BC = 2BD = 217.25 = 34.5 cm.

Next, we need to find the area (K) of triangle ABC. We can use Heron's formula, which states that the area of a triangle with sides a, b, and c is given by:

K = sqrt[s(s - a)(s - b)(s - c)]

where s is the semi-perimeter of the triangle, given by s = (a + b + c)/2. So, we have:

s = (17.5 + 17.5 + 34.5)/2 = 34.75 cm K = sqrt[34.75(34.75 - 17.5)(34.75 - 17.5)(34.75 - 34.5)] = 76.5 cm^2

Finally, we can substitute these values into the formula for the radius of the circumcircle to find:

R = (17.517.534.5)/(4*76.5) = 26.25 cm

So, the radius of the circle circumscribing the triangle ABC is 26.25 cm. The correct answer is (D) 26.25.