Bissoy.com
Doctors Medicines MCQs Q&A

As shown in the figure, a semicircle is inscribed in a triangle with sides 22, 26 and 40 cm. Find the diameter of the semicircle.

As shown in the figure, a semicircle is inscribed in a triangle with sides 22, 26 and 40 cm. Find the diameter of the semicircle. Correct Answer 22 cm

/ = 4/5

Since cosC = 4/5

⇒ sinC = 3/5

In triangle COP

sinC = OP/OC

⇒ 3/5 = OP/ (55/3)

⇒ OP = 11

∴ Diameter of the semicircle = 2OP = 22 cm

Related Questions

A circle of maximum area is inscribed in the square. An equilateral triangle is inscribed in that circle and all the vertices of the triangle touch the circle. A triangle is formed by the joining of the midpoint of the sides of the equilateral triangle. Find the ratio of the area of the square and area of the triangle which is formed by midpoints.
A semicircle is inscribed inside a rectangle in such a way, so that the diameter of the semicircle coincides with the length of the rectangle. If the area of the semicircle is 50 π, then what is the area of the rectangle?
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues uptofive times. What is the ratio of the area of fourth triangle to that of sixth triangle? (Original triangle is counted as 1st triangle)
The perimeter of the square is equal to the perimeter of the semicircle. The sum of the perimeter of semicircle and square is 72 cm, then, what is the ratio of the area of the semicircle and the area of the square?
Consider the statements given below- A: Inradius of circle which is inscribed inside a triangle is obtained when area of triangle is divided by its perimeter. B: Triangle formed in a major arc of a circle is an acute angle triangle. C: Largest possible chord of a circle is always less than its diameter. Which of the above statement(s) is/are TRUE?
A semicircle is drawn on the longer diagonal of a cube and a triangle of the largest possible area is constructed on the shorter diagonal of the same cube. what is the ratio of the areas of the semicircle and the triangle? 
Consider the following statements :I. Three sides of a triangle are equal to three sides of another triangle, then the triangles are congruent.II. If three angles of a triangle are respectively equal to three angles of another triangle, then the two triangles are congruent.Of these statements :
A circle is inscribed in an equilateral triangle and a square is inscribed in the circle. Then, find the ratio between the area of the square and the area of the equilateral triangle?
In an equilateral triangle, another equilateral triangle is drawn inside joining the mid-points of the sides of the given equilateral triangle and the process continues up to seven times. What is the ratio of the area of fourth triangle to that of seventh triangle?
An equilateral triangle ABC is inscribed in a circle as shown in the figure. A square of the largest possible area is made inside this triangle as shown. Another circle made inscribing the square. What is the ratio of the area of the small circle and the large circle?