SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Important Questions for Geometry Mathematics 2

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.

If A(–14, –10), B(6, –2) is given, find the coordinates of the points which divide segment AB into four equal parts.

If A (20, 10), B(0, 20) are given, find the coordinates of the points which divide segment AB into five congruent parts.

The line segment AB is divided into five congruent parts at P, Q, R and S such that A–P–Q–R–S–B. If point Q(12, 14) and S(4, 18) are given find the coordinates of A, P, R, B.

AB and AC are the two chords of a circle whose radius is r. If p and q are
the distance of chord AB and CD, from the centre respectively and if
AB = 2AC then proove that 4q2 = p² + 3r².

Δ SHR ∼ Δ SVU. In Δ SHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and
SHSV = 53 then draw Δ SVU.

Distance of point (−3, 4) from the origin is ______.