In the figure 7.46, if O is the centre of the circle, PQ is a chord. ∠ POQ = 90°, area of shaded region is 114 cm², find the radius of the circle. (π = 3.14)

Choose the correct alternative answer for each of the following question.

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

∆ LMN is an equilateral triangle. LM = 14 cm. As shown in figure, three sectors are drawn with vertices as centre and radius7 cm. Find,

(1) A (Δ LMN)

(2) Area of any one of the sectors

(3) Total area of all three sectors

(4) Area of shaded region

A chord PQ of a circle with radius 15 cm subtends an angle of 60° with the centre of the circle. Find the area of the minor as well as the major segment. (π = 3.14)

Radius of a sector of a circle is 7 cm. If measure of arc of the sector is –

(l) 30°

(ll) 210°

(lll) three right angles

Find the area of sector in each case.

In the figure 7.45, if A is the centre of the circle. ∠ PAR = 30°, AP = 7.5, find the area of the segment PQR. (π = 3.14)

Choose the correct alternative answer for each of the following question.

If measure of an arc of a circle is 160° and its length is 44 cm, find the circumference of the circle.

In figure 7.43, A is the centre of the circle. ∠ ABC = 45° and AC = 7√2 cm. Find the area of segment BXC.

In figure 7.33 O is the centre of the sector.∠ ROQ = ∠ MON = 60°. OR = 7 cm, and OM = 21 cm. Find the lengths of arc RXQ and arc MYN.

Radius of a sector of a circle is 3.5 cm and length of its arc is 2.2 cm. Find the area of the sector.

In the figure 7.47, seg AB is a chord of a circle with centre P. If PA = 8 cm and distance of chord AB from the centre P is 4 cm, find the area of the shaded portion.