In the figure, a semicircle with its diameter on thehypotenuse of a ri

1.	In the figure, a semicircle with its diameter on thehypotenuse of a right angled triangle is showntouching the remaining sides of a triangle. Theparts of the hypotenuse made by the centre of thesemicircle have lengths 15 cm and 20 cmrespectively. Find the radius of the semicircle.(Construction : Join OD and OE)
Answer» Step-by-step explanation: Let the length shown in above diagram be T. The power of circle T 2 =(15−R)(15+R) From SIMILAR triangles (radius / hypotenuse) of right SIDE right angled triangle = R T = 20 15 = 4 3 SOLVING R=12 T=9 Arc length in quarter circle = 2 πR = 2 π.12 =6π. *Hope* *this will* *HELP you* *Mark me* *as brilliant*

In the figure, a semicircle with its diameter on thehypotenuse of a right angled triangle is showntouching the remaining sides of a triangle. Theparts of the hypotenuse made by the centre of thesemicircle have lengths 15 cm and 20 cmrespectively. Find the radius of the semicircle.(Construction : Join OD and OE)

Answer»

Step-by-step explanation:

Let the length shown in above diagram be T.

The power of circle T

=(15−R)(15+R)

From SIMILAR triangles (radius / hypotenuse) of right SIDE right angled

triangle =

SOLVING R=12 T=9

Arc length in quarter circle =

πR

π.12

=6π.

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