In the given figure, ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r. Which of the following is the area of the triangle ?

Question

In the given figure, ABC is an equilateral triangle which is inscribed inside a circle and whose radius is r. Which of the following is the area of the triangle ?

$${\left( {r + DE} \right)^{\frac{1}{2}}}{\left( {r - DE} \right)^{\frac{3}{2}}}$$
$${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^2}$$
$${\left( {r - DE} \right)^2}{\left( {r + DE} \right)^2}$$
$${\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^{\frac{3}{2}}}$$

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

Related Questions

An equilateral triangle is described on the diagonal of a square. What is the ratio of the area of the triangle to that of the square ?

1 Answers 4 Views

When the addenda on pinion and wheel is such that the path of approach and path of recess are half of their maximum possible values, then the length of the path of contact is given by (where r = Pitch circle radius of pinion, R = Pitch circle radius of wheel and $$\varphi $$ = Pressure angle)?

1 Answers 14 Views

ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?

1 Answers 4 Views

The radius of a friction circle for a shaft rotating inside a bearing is (where r = Radius of shaft and $$\tan \varphi $$ = Coefficient of friction between the shaft and bearing)?

1 Answers 15 Views

The heat transfer by conduction through a thick cylinder (Q) is given by (where T₁ = Higher temperature, T₂ = Lower temperature, r₁ = Inside radius, r₂ = Outside radius, l = Length of cylinder, and k = Thermal conductivity)?

1 Answers 5 Views

Consider the following statements : I. Every equilateral triangle is necessarily an isosceles triangle. II. Every right-angled triangle is necessarily an isosceles triangle. III. A triangle in which one of the median is perpendicular to the side it meets, is necessarily an isosceles triangle. The correct statements are:?

1 Answers 4 Views

ABC is an equilateral triangle. Points D, E and F are taken as the mid-point on sides AB, BC, AC respectively, so that AD = BE = CF. Then AE, BF, CD enclosed a triangle which is:?

1 Answers 4 Views

If a parallelogram with area P, a rectangle with area R and a triangle with area T are all constructed on the same base and all have the same altitude, then which of the following statements is false ?

1 Answers 4 Views

Direction : Two statements I and II are given. These statement may be either independent causes or may be effects of independent causes or a common cause. One of these statements may be the effect of the other statements. Read both the statements and decide which of the following answer choice correctly depicts the relationship between these two statements. Mark answer : I. The university authority has instructed all the colleges under its jurisdiction to ban use of all phones inside the college premises. II. Majority of the teachers of the colleges signed a joint petition to the university complaining the disturbances caused by cell phone ring-tones inside the classrooms.?

1 Answers 5 Views

For a ternery mixture, in which equilateral triangular co-ordinate is used in leaching and extraction, a __________ of the equilateral triangular co-ordinates.?

1 Answers 5 Views

AhmedNazir · Accepted Answer · 2022-09-01T13:21:41+06:00

Answer: Option 4

We have : $$\eqalign{ & AE \bot BC{\text{ and }} \cr & AD = BD = CD = r \cr & AE = AD + DE = r + DE \cr} $$ In Δ BDC, $$\eqalign{ & BE = \sqrt {{{\left( {BD} \right)}^2} - {{\left( {DE} \right)}^2}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \sqrt {{r^2} - {{\left( {DE} \right)}^2}} \cr & \,\,\,\,\,\,\,\,\,\,\, = \sqrt {\left( {r - DE} \right)\left( {r + DE} \right)} \cr} $$ ∴ Area of the triangle : $$\eqalign{ & = \frac{1}{2} \times BC \times AE \cr & = \frac{1}{2} \times 2BE \times AE \cr & = BE \times AE \cr & = \sqrt {\left( {r - DE} \right)\left( {r + DE} \right)} \left( {r + DE} \right) \cr & = {\left( {r - DE} \right)^{\frac{1}{2}}}{\left( {r + DE} \right)^{\frac{3}{2}}} \cr} $$