A chord AB divides a circle of radius 4 cm into two segments. If AB subtends a central angle of 60°, find the area of the minor segment.

Step-by-step explanation:

The diagram of the circle is shown in the attached photo.

Looking at triangle AOB, 2 sides are equal. It means that A= B.

Therefore, A = B = (180 - 60)/2 = 60

Therefore, triangle AOB is an equilateral triangle. AB = AO = BO = 4 cm

We would find the area of triangle AOB by applying heron's formula

Area = √s(s - a)(s - b)(s - c)

s = (a + b + c)/2 = (4 + 4 + 4)/2 = 6

Area = √6(6 - 4)(6 - 4)(6 - 4)

Area = √48 = 6.93cm²

Area of sector formed by the minor segment = area of triangle + area of minor segment

Area of sector = 60/360 × 3.14 × 4² = 8.37 cm²

Area of minor segment = 8.37 - 6.93 = 1.44 cm²

solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.

you have to put the graph on here with the question

step-by-step explanation: