Bissoy.com
Doctors Medicines MCQs Q&A

Inside a right-angled triangle, a circle is drawn which touches all the three sides of the triangle. If the two sides of the triangle other than hypotenuse are 5 cm and 12 cm then find the radius of the circle drawn?

Inside a right-angled triangle, a circle is drawn which touches all the three sides of the triangle. If the two sides of the triangle other than hypotenuse are 5 cm and 12 cm then find the radius of the circle drawn? Correct Answer 2 cm

GIVEN:

Two sides of the triangle other than hypotenuse are 5 cm and 12 cm.

FORMULA USED:

Pythagoras theorem:

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

And

Area of a triangle = 1/2 × Base × Height

CALCULATION:

Shortcut Trick

Radius of incircle, r = Area/Semi-perimeter = (½ × 12 × 5)/ = 2 cm

Related Questions

Which of the following statements is/are true? A: If a circle is formed from a wire, which was initially in the shape of a semi-circle, then ratio of radius of circle and that of semi-circle will be 7: 11. B: If in a semi-circle of radius ‘r’, another semi-circle of radius ‘4r/5’ is drawn, then area of the remaining part of larger semi-circle will be ‘3πr2/5’. C: In a circle of radius ‘r’, if ‘O’ is the center of circle and radii OA and OB are at the angle of 45°, then the length of major arc AB will be ‘7πr/8’.
If a square of a side 20 m is folded along one of its diagonal to form a triangle which is again folded along perpendicular drawn on hypotenuse and similarly once again folded along perpendicular drawn on hypotenuse. Then find hypotenuse of smallest triangle? 
A tangent is drawn from a point p outside the circle, which touches the circle at point A and B, another tangent is drawn from a point E on the circumference on the circle, which touches the line PA and PB at C and D, if PC measures 8 cm, PD measures 9 cm and CD measures 7 cm, then find the radius of circle.
PAB is a tangent which is common to two circles which touches each other at point X. The tangent touches the smaller circle at A and larger circle at B. If PA = 20 cm and the radius of smaller circle is 15 cm, then find the radius of larger circle.
A ΔABC has sides 5 cm, 6 cm and 7 cm. Side BC of the triangle touches the circle, AB when extended touches the circle at P and AC when extended touches the same circle at Q. Find the length (in cm) of AQ.
“What is the different between height and radius of solid cylinder?” Which of the following option is sufficient alone to find the answer? A) A solid cylinder is made by melting a solid sphere. The radius of cylinder is 3 times the radius of a circle whose area is 154 sq.m. Height of cylinder is equal to the height of cone whose volume is 2772 cubic meters. B) Area of a rectangle whose longer side is ¾ times the radius of a solid cylinder, is 168 sq.m and, Volume of solid cylinder is 2772 cubic meters and its height is 18 m. C) A metallic cone of radius 15m and height 35m is melted into the solid cylinder of radius equal to the radius of a circle whose area is equal to the area of rectangle whose sides are in the ratio 4 : 3 respectively. D) The curved surface area of the solid cylinder is 3 time the surface area of a sphere of radius 7m and height of cylinder is equal to the height of a metallic cone whose curved surface area is 308 sq.m. 
a, b and c are the sides of a right triangle with c as hypotenuse. The radius r, of the circle which touches the three sides of the triangle is :
Which two classes use the Shape class correctly?
A. public class Circle implements Shape { private int radius; }B. public abstract class Circle extends Shape { private int radius; }C. public class Circle extends Shape { private int radius; public void draw(); }D. public abstract class Circle implements Shape { private int radius; public void draw(); }E. public class Circle extends Shape { private int radius; public void draw() { /* code here */ } }F. public abstract class Circle implements Shape { private int radius; public void draw() { /* code here */ } }
A = Area of the largest circle drawn inside a square of side 1 cm. B = Sum of areas of 4 identical (largest possible) circles drawn inside a square of side 1 cm. C = Sum of areas of 9 identical circle (largest possible) drawn inside a square of side 1 cm. D = Sum of area of 16 identical circles (largest possible) drawn inside a square of side 1 cm. Which of the following is TRUE about A, B, C and D?
Two right angled triangles are congruent if :
I. The hypotenuse of one triangle is equal to the hypotenuse of the other.
II. A side for one triangle is equal to the corresponding side of the other.
III. Sides of the triangles are equal.
IV. An angle of the triangle are equal.
Of these statements, the correct ones are combination of: