LET ABCD be a quadrilateral with area 18 ,with side AB parallel to the side CD and AB=2CD .Let AD be perpendicular to AB and CD .If a circle is drawn inside the quadrilateral ABCD touching all the side ,then it's radius is A 3 B 2 C 3/2 D 1?
Ref: https://edurev.in/question/547474/LET-ABCD-be-a-quadrilateral-with-area-18-with-side-AB-parallel-to-the-side-CD-and-AB2CD-Let-AD-be-
Let CD=x then AB=2CD=2x.Let r be the radius of the circle inscribed in the quadrilateral ABCD.
Given: Area of quadrilateral ABCD=18 and ABis|| to CD.
⇒ 1/2(x+2x).2r=18
⇒ 3xr=18
⇒ xr=6-----(1)
OP=OM=PD=OQ=AM=r
⇒ PC=x−randMB=2x−r
Let ∠PCO=angleOCQ=θ then from right-angled ΔOPC
From (1) & (4) we get,
xr=6
3rr^2=6
r^2=4
r=2
Hence (b) is the correct answer.
FAQs on MCQ: Trigonometry, MAthematics JEE
| 1. What is Trigonometry? |  |
Ans. Trigonometry is a branch of mathematics that deals with the relationships between the angles and sides of triangles. It involves the study of trigonometric functions such as sine, cosine, and tangent, and their applications in various fields such as physics, engineering, and astronomy.
| 2. What are the basic trigonometric functions? | |
Ans. The basic trigonometric functions are sine, cosine, and tangent. Sine (sin) of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. Cosine (cos) of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. Tangent (tan) of an angle is defined as the ratio of the length of the side opposite the angle to the length of the adjacent side.
| 3. How are trigonometric functions used in real life? | |
Ans. Trigonometric functions have various real-life applications. For example, in physics, they are used to describe the motion of objects in simple harmonic motion or waves. In engineering, trigonometry is used to calculate forces, angles, and distances in structural design and construction. Trigonometry also plays a significant role in navigation, astronomy, and electrical engineering.
| 4. What are the trigonometric identities? | |
Ans. Trigonometric identities are equations that are true for all values of the variables involved. Some of the commonly used trigonometric identities include the Pythagorean identities (sin²θ + cos²θ = 1), the reciprocal identities (cosecθ = 1/sinθ, secθ = 1/cosθ, cotθ = 1/tanθ), and the quotient identities (tanθ = sinθ/cosθ, cotθ = cosθ/sinθ).
| 5. How can trigonometry be used to solve triangles? | |
Ans. Trigonometry can be used to solve triangles by applying the laws of sines and cosines. The law of sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. The law of cosines relates the lengths of the sides of a triangle to the cosine of one of its angles. By using these laws and trigonometric functions, we can determine the lengths of the sides and the measures of the angles of a triangle.
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