SSC (English Medium) 10th Standard - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then

1. What is the length of each tangent segment?
2. What is the measure of ∠MRO?
3. What is the measure of ∠MRN?

Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON with the help of activity.

In the given figure, the circles with centres A and B touch each other at E. Line l is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii of the circles are 4 cm, 6 cm. 

In the given figure, O is the centre of the circle and B is a point of contact. seg OE ⊥ seg AD, AB = 12, AC = 8, find (1) AD (2) DC (3) DE.

In the given figure, seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DE × GE = 4r²

Four alternative answers for the following question is given. Choose the correct alternative.
 Length of a tangent segment drawn from a point which is at a distance 12.5 cm from the centre of a circle is 12 cm, find the diameter of the circle.

Four alternative answers for the following question is given. Choose the correct alternative.

 Seg XZ is a diameter of a circle. Point Y lies in its interior. How many of the following statements are true ? (i) It is not possible that ∠XYZ is an acute angle. (ii) ∠XYZ can’t be a right angle. (iii) ∠XYZ is an obtuse angle. (iv) Can’t make a definite statement for measure of ∠XYZ.

In the given figure, M is the centre of the circle and seg KL is a tangent segment.
If MK = 12, KL = \[6\sqrt{3}\] then find –
(1) Radius of the circle.
(2) Measures of ∠K and ∠M.

In the given figure, O is the centre of the circle. Seg AB, seg AC are tangent segments. Radius of the circle is r and `l`(AB) = r, Prove that ▢ABOC is a square. 

Proof: Draw segment OB and OC.

`l`(AB) = r   ...[Given] (i)

AB = AC   ...[`square`] (ii)

But OB = OC = r   ...[`square`] (iii)

From (i), (ii) and (iii)

AB = `square` = OB = OC = r

∴ Quadrilateral ABOC is `square`

Similarly, ∠OBA = `square`   ...[Tangent Theorem]

If one angle of `square` is right angle, then it is a square.

∴ Quadrilateral ABOC is a square.

The radius of a circle is 10 cm. The measure of an arc of the circle is 54^°. Find the area of the sector associated with the arc. (\[\pi\]= 3.14 )

The measure of an arc of a circle is 80° and its radius is 18 cm. Find the length of the arc. (π = 3.14)

Area of a sector of a circle of radius 15 cm is 30 cm². Find the length of the arc of the sector.

The area of a sector of a circle of 6 cm radius is 15 π sq. cm. Find the measure of the arc and the length of the arc corresponding to the sector.

In the given figure, 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. ( \[\pi\] = 3.14, \[\sqrt{3}\]= 1.73 )

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region 

In Δ ABC, if ∠ A = 65° ; ∠ B = 40° then find the measure of ∠ C.

Length of a rectangular tank is twice its breadth. If the
depth of the tank is 3 m and area of its four walls is 108 m2, find the
length of the tank.

In the following figure ‘O’ is the centre of the circle.

∠AOB = 1100, m(arc AC) = 450.

Use the information and fill in the boxes with proper numbers.

(i) m(arcAXB) =

(ii)m(arcCAB) =
(iv)∠COB =

(iv)m(arcAYB) =

Find the length of an arc if measure of the arc is 90° and its radius
is 14 cm.

Measure of an arc of a sector of a circle is 900 and its radius is 7cm. Find the perimeter of the sector.
(A) 44 cm (B) 25 cm (C) 36 cm (D) 56 cm