SSC (English Medium) 10th Standard - Maharashtra State Board Important Questions for Geometry Mathematics 2

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, 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.

`square`PQRS is a parallelogram. Write the sum of measures of ∠P and ∠ Q.

From the information given in the figure, find the measure of ∠ AEC.

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 equation of a lined passage through (3,6) and making intercepts equal magnitude but opposite in sign-on both the axes. 

The perpendicular height of a cone is 12 cm and its slant height is 13 cm. Find the radius of the base of the cone. 

Choose the correct alternative: 
If the points, A, B, C are non-collinear points, then how many circles can be drawn which passes through points A, B, and C? 

In the above figure, the circles with P, Q, and R intersect at points B, C, D, and E as shown. Lines CB and ED intersect in point M. Lines are drawn from point M to touch the circles at points A and F. Prove that MA = MF. 

In the figure given above, O is the centre of the circle. Using given information complete the following table:

In the given figure, M is the centre of the circle and seg KL is a tangent segment. L is a point of contact. If MK = 12, KL = `6sqrt3`, then find the radius of the circle.

The chords corresponding to congruent arcs of a circle are congruent. Prove the theorem by completing following activity.

Given: In a circle with centre B 

arc APC ≅ arc DQE

To Prove: Chord AC ≅ chord DE

Proof: In ΔABC and ΔDBE,

side AB ≅ side DB   ...`square`

side BC ≅ side `square`   ...`square`

∠ABC ≅ ∠DBE   ...[Measure of congruent arcs]

∆ABC ≅ ∆DBE   ...`square`

If AB and CD are the common tangents in the circles of two unequal (different) radii, then show that seg AB ≅ seg CD.

Prove that, tangent segments drawn from an external point to the circle are congruent.

In a parallelogram ABCD, ∠B = 105°. Determine the measure of ∠A and ∠D.

In the following figure, XY = 10 cm and LT = 4 cm. Find the length of XT.

Find the value of y, if the points A(3, 4), B(6, y) and C(7, 8) are collinear.

A pizza has 8 slices all equally spaced. Suppose pizza is a flat circle of radius 28 cm, find the area covered between 3 slices of pizza.

A circle touches side BC at point P of the ΔABC, from outside of the triangle. Further extended lines AC and AB are tangents to the circle at N and M respectively. Prove that : AM = `1/2` (Perimeter of ΔABC)