Circle – Maharashtra Board Class 7 Solutions for Mathematics

Circle – Maharashtra Board Class 7 Solutions for Mathematics (English Medium)

MathematicsGeneral ScienceMaharashtra Board Solutions

Exercise 90:

Solution 1:

• Centre of the circle: Point C

Diameters of the circle: Seg PQ and Seg RS
Chord of the circle: Seg RQ

• Points in the interior of the circle: Points C and M.
• Points in the exterior of the circle: Points K and N.
• Points on the circle: Points P, R, Q and S.

Exercise 91:

Solution 1:

1. The two segments of the circle made by the diameter are called semicircular region.
2. The measure of an angle in a semicircular region is 90 degrees.
3. All the points on the circle and all points in the interior of the circle together form the circular region.

Solution 2:

• False.

Correct statement: An angle in a semicircular region is a right angle.

• False.

Correct statement: The angle in a minor segment of a circle is an obtuse angle.

• False.

Correct statement: The angle in a major segment of a circle is an acute angle.

• True.

Solution 3:

• The angles in the minor segment are ∠PAQ and ∠PBQ.
• The angles in the major segment are ∠PDQ and ∠PCQ.
• The pairs of angles in the minor segment PRQ are ∠PAQ and ∠PBQ and the pairs of angles in the major segment are ∠PDQ and ∠PCQ.

Solution 4:

• Seg SK is the diameter of the given circle, and hence divides the circle into two semicircular regions.

Now, an angle in a semicircular region is a right angle.

Hence, m∠STK = 90°

• ∠SMK also is an angle in the semicircular region.

Hence, m∠SMK = 90°

Solution 5:

∠XYZ and ∠XPZ are the angles in the same segment and angles in the same segment are congruent.
Hence ∠XYZ and ∠XPZ have equal measures.

∴ m∠XYZ = m∠XPZ = 100°

Solution 6:

∠XYZ and ∠XPZ are the angles in the same segment and angles in the same segment are congruent.
Hence ∠XYZ and ∠XPZ have equal measures.

∴ m∠XYZ = m∠XPZ = 100°