SSC (English Medium) 10th Standard - Maharashtra State Board Important Questions

In the above figure, ∠L = 35°, find :

1. m(arc MN)
2. m(arc MLN)

Solution :

1. ∠L = `1/2` m(arc MN) ............(By inscribed angle theorem)
   ∴ `square = 1/2` m(arc MN)
   ∴ 2 × 35 = m(arc MN)
   ∴ m(arc MN) = `square`
2. m(arc MLN) = `square` – m(arc MN) ...........[Definition of measure of arc]
   = 360° – 70°
   ∴ m(arc MLN) = `square`

In the above figure, ∠ABC is inscribed in arc ABC.

If ∠ABC = 60°. find m ∠AOC.

Solution:

∠ABC = `1/2` m(arc AXC)   ......`square`

60° = `1/2` m(arc AXC) 

`square` = m(arc AXC) 

But m ∠AOC = \[\boxed{m(arc ....)}\]   ......(Property of central angle)

∴ m ∠AOC = `square`

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.

Draw `angle ABC` of measure 80° and bisect it

Draw ∠ABC of measures 135^°and bisect it.

∆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.

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.

Ponit M is the mid point of seg AB and AB = 14 then AM = ?

Observe the adjoining figure and write down one pair of interior angles.

If Δ ABC ∼ Δ XYZ then complete the following brackets.
`(AB)/(XY) =  /(YZ) = (AC)/`

Draw ∠ ARP= 115° and bisect it.

Write down the equation of X- axis.

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.

Draw seg AB of length 5.7 cm and bisect it.