###### Advertisements

###### Advertisements

In the following figure, if m(are DXE) = 90° and m(are AYC) = 30°. Find ∠DBE.

###### Advertisements

#### Solution

By inscribed angle theorem,

m∠AEB=(1/2) × m∠AYC=(1/2) × 30^{o} = 15^{o }...(1)

m∠EAD=(1/2) × m∠DXE=(1/2) × 90^{o} = 45^{o} ...(2)

∠DBE + ∠AEB = ∠EAD

⇒ m∠DBE + 15^{o} = 45^{o}

⇒ m∠DBE = 45^{o} - 15^{o} = 30^{o}

#### APPEARS IN

#### RELATED QUESTIONS

Find the area of sector whose arc length and radius are 10 cm and 5 cm respectively

Find the area of the sector whose arc length and radius are 14 cm and 6 cm respectively.

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find.

- The total length of the silver wire required.
- The area of each sector of the brooch [Use π = `22/7`]

Area of a sector of angle p (in degrees) of a circle with radius R is ______.

In the given figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the shaded region.

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circles are drawn touching each other with the vertices as their centres. Find the radii of the three circles.

The area of sector of circle of radius 2cm is 𝜋cm2. Find the angle contained by the sector.

In a circle of radius 35 cm, an arc subtends an angle of 72° at the centre. Find the length of arc and area of sector

The diagram shows a sector of circle of radius ‘r’ can containing an angle 𝜃. The area of sector is A cm2 and perimeter of sector is 50 cm. Prove that

(i) 𝜃 =`360/pi(25/r− 1)`

(ii) A = 25r – r^{2}

AB is the diameter of a circle, centre O. C is a point on the circumference such that ∠COB = 𝜃. The area of the minor segment cutoff by AC is equal to twice the area of sector BOC.Prove that `"sin"theta/2. "cos"theta/2= pi (1/2−theta/120^@)`

The radius of a circle is 10 cm. The area of a sector of the sector is 100 cm^{2}. Find the area of its corresponding major sector. ( \[\pi\] = 3.14 ).

^{°},

In the given figure, radius of circle is 3.4 cm and perimeter of sector P-ABC is 12.8 cm . Find A(P-ABC).

(2) Area of any one of the sectors

In the given figure, A is the centre of the circle. ∠ABC = 45^{° }and AC = 7√2 cm. Find the area of segment BXC.

In the given figure, if A is the centre of the circle. \[\angle\] PAR = 30^{°}, AP = 7.5, find the area of the segment PQR ( \[\pi\] = 3.14)

In the given figure, if O is the centre of the circle, PQ is a chord. \[\angle\] POQ = 90^{°}, area of shaded region is 114 cm^{2} , find the radius of the circle. \[\pi\] = 3.14)

In the given figure, if O is the centre of the circle, PQ is a chord. \[\angle\] POQ = 90^{°}, area of shaded region is 114 cm^{2} , find the radius of the circle. \[\pi\] = 3.14)

In the given figure, if O is the center of the circle, PQ is a chord. \[\angle\] POQ = 90^{°}, area of the shaded region is 114 cm^{2}, find the radius of the circle. \[\pi\] = 3.14)

Choose the correct alternative answer for the following question.

Find the perimeter of a sector of a circle if its measure is 90^{°} and radius is 7 cm.

A chord 10 cm long is drawn in a circle whose radius is `5sqrt(2)` cm. Find the areas of both the segments.

In following fig., ABCD is a square. A cirde is drawn with centre A so that it cuts AB and AD at Mand N respectively. Prove that Δ DAM ≅ Δ .BAN.

A chord of length 6 cm is at a distance of 7.2 cm from the centre of a circle. Another chord of the same circle is of length 14.4 cm. Find its distance from the centre.

Prove that the circle drawn with any side of a rhombus as a diameter, passes through the point of intersection of its diagonals.

In following figure , C is a point on the minor arc AB of the circle with centre O . Given ∠ ACB = p° , ∠ AOB = q° , express q in terms of p. Calculate p if OACB is a parallelogram.

In following fig., PT is a tangent to the circle at T and PAB is a secant to the same circle. If PA = 4cm and AB = Scm, find PT.

In the following figure, if m(arc DXE) = 120° and m(arc AYC) = 60°. Find ∠DBE.

Find the area of a sector of a circle having radius 6 cm and length of the arc 15 cm.

The diameter of a sphere is 6 cm, Find the total surface area of the sphere. (π = 3.14)

Radius of a circle is 10 cm. Measure of an arc of the circle is 54°. Find the area of the sector associated with the arc. (π = 3.14)

**Given: **The radius of a circle (r) = `square`

Measure of an arc of the circle (θ) = `square`

Area of the sector = `θ/360^circ xx square`

= `square/360^circ xx square xx square xx square`

= `square xx square xx square`

= 47.10 cm^{2}

With vertices A, B and C of ΔABC as centres, arcs are drawn with radii 14 cm and the three portions of the triangle so obtained are removed. Find the total area removed from the triangle.

The area of the sector of a circle of radius 12 cm is 60π cm^{2}. The central angle of this sector is ______.