**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°