SSC (Marathi Semi-English) इयत्ता १० वी - Maharashtra State Board Important Questions

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)

Draw an equilateral ΔABC with side 6.2 cm and construct its circumcircle

Find the length of the altitude of an equilateral triangle with side 6 cm.

Draw a triangle ABC with side BC = 6cm, ∠B = 45° and ∠A = 100°, then construct a triangle PBQ whose sides are `7/4` times the corresponding sides of ΔABC.

Draw ΔRSP ∼ ΔTQP. In ΔTQP, TP = 5 cm, ∠P = 50°, PQ = 4.5 cm and `("RS")/("TQ") = 2/3`.

Construct any ΔABC. Construct ΔA'BC' such that AB : A'B = 5 : 3 and ΔABC ∼ ΔA'BC'.

Construct the circumcircle and incircle of an equilateral triangle ABC with side 6 cm and centre O. Find the ratio of radii of circumcircle and incircle.

∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm, `(AM)/(AH) = 7/5`. Construct ∆AHE.

∆ABC ~ ∆LBN. In ∆ABC, AB = 5.1 cm, ∠B = 40°, BC = 4.8 cm, \[\frac{AC}{LN} = \frac{4}{7}\]. Construct ∆ABC and ∆LBN.

Construct ∆PYQ such that, PY = 6.3 cm, YQ = 7.2 cm, PQ = 5.8 cm. If \[\frac{YZ}{YQ} = \frac{6}{5},\] then construct ∆XYZ similar to ∆PYQ.

Find the distance between the following pairs of point.

W `((- 7)/2 , 4)`, X (11, 4)

Determine whether the points are collinear.

P(–2, 3), Q(1, 2), R(4, 1)

Show that the points A(1, 2), B(1, 6), C(1 + 2`sqrt3`, 4) are vertices of an equilateral triangle.