# A circle is inscribed in a right triangle. The length of the radius of the circle is 6 cm, and the length of the hypotenuse is 29 cm. Find the lengths of the two segments of the hypotenuse that are determined by the point of tangency. Question
Analytic geometry A circle is inscribed in a right triangle. The length of the radius of the circle is 6 cm, and the length of the hypotenuse is 29 cm. Find the lengths of the two segments of the hypotenuse that are determined by the point of tangency. 2021-02-04
Similar to circle sphere is a two dimensional space where the set of points that are at the same distance r from a given point in a three dimensional space. In analytical geometry with a center and radius is the locus of all points is called sphere Given: A circle is inscribed in a right triangle. The length of the radius of the circle is 6 cm, and the length of the hypotenuse is 29 cm. thus the given condition is can be drawn as follows, The objective is to find the lengths of the two segments of the hypotenuse that are determined by the point of the tangency Using Pythagorean theorem, $$AC^{2} = AB^{2} + BC^{2}$$
$$AC^{2} = (AE + EB)^{2} + (BF + FC)^{2}$$
$$29^{2} = (X + 6)^{2} + (6 + 29 - X)^{2}$$
$$29^{3} = (X + 6)^{2} + (35 - X)^{2}$$
$$841 = 2X^{2} - 58X + 1261$$ On solving further $$2x^{2} -58x + 420 = 0$$
$$x(x - 14) - 15x + 210 = 0$$
$$(x - 15)(x - 14) = 0$$ Here $$x = 15 or x = 14$$ Therefore, the lengths of the two segments are as follows, 15 and 14 cm

### Relevant Questions Two right triangles are similar. The legs of the smaller triangle have lengths of 3 and 4. The scale factor is 1:3. Find the length of the hypotenuse of the larger triangle. The vertices of a tetrahedron correspond to four alternating corners of a cube. By using analytical geometry, demonstrate that the angle made by connecting two of the vertices to a point at the center of the cube is $$\displaystyle{109.5}^{\circ}$$, the characteristic angle for tetrahedral molecules. An equilateral triangle is inscribed in a circle of radius 4r. Express the area A within the circle but outside the triangle as a function of the length 5x of the side of the triangle. Given a right triangle. One of the angles is $$\displaystyle{20}^{\circ}$$. Find the other 2 angles. Consider rectangel CREB that is formed of squares COAB and OREA, where AE=4ft. Assume squares COAB and OREA are congruent.
BO=3m-2n
AR=7(m-1)-4.8n
Determine the values of m and n and the length of RB. The minute hand of a clock is 6 inches long and moves from 12 to 4 o'clock. How far does the tip of the minute hand move? Express your answer in terms of $$\displaystyle\pi$$ and then round to two decimal places. Point K is on line segment ‾JL. Given JK = 2x - 2, KL = x - 9, and JL = 2x + 8, determine the numerical length of ‾KL. a. The radial vector field $$\displaystyle{F}={\left\langle{x},{y}\right\rangle}$$
b. The rotation vector field $$\displaystyle{F}={\left\langle-{y},{x}\right\rangle}$$  