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:
- The two segments of the circle made by the diameter are called semicircular region.
- The measure of an angle in a semicircular region is 90 degrees.
- 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°