Geometry Shaalaa.com Model Set 2 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

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

Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle?

6 cm 

12 cm 

24 cm

can’t say 

 If in ∆DEF and ∆PQR, ∠D ≅ ∠Q, ∠R ≅ ∠E then which of the following statements is false? 

\[\frac{EF}{PR} = \frac{DF}{PQ}\] 

\[\frac{DE}{PQ} = \frac{EF}{RP}\] 

\[\frac{DE}{QR} = \frac{DF}{PQ}\] 

\[\frac{EF}{RP} = \frac{DE}{QR}\]

Some question and their alternative answer are given. Select the correct alternative.

If a, b, and c are sides of a triangle and a² + b² = c², name the type of triangle.

Obtuse angled triangle

Acute angled triangle 

Right-angled triangle

Equilateral triangle

Select the correct alternative for the following question.

The number of tangents that can be drawn to a circle at a point on the circle is ............... .

3

2

1

0

Prove that:

\[\cos^2 \theta\left( 1 + \tan^2 \theta \right) = 1\]

Find the volume of a cone if the radius of its base is 1.5 cm and its perpendicular height is 5 cm.

In the given figure, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4, MD = 8 find DN
(2) If RS = 18, MD = 9, DN = 8 find DS

In the given figure, if AB || CD || FE then Find x and AE.   

Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?

Determine whether the point is collinear.
A(1, –3), B(2, –5), C(–4, 7)

If \[\sec\theta = \frac{13}{12}\], find the values of other trigonometric ratios.

In the given figure, altitudes YZ and XT of ∆WXY intersect at P. Prove that,
(1) ▢WZPT is cyclic.
(2) Points X, Z, T, Y are concyclic.

Prove that `(sinθ - cosθ + 1)/(sinθ + cosθ - 1) = 1/(secθ - tanθ)`

For finding AB and BC with the help of information given in the figure, complete following activity.

AB = BC ..........

\[\therefore \angle BAC = \]

\[ \therefore AB = BC =\] \[\times AC\]

\[ =\] \[\times \sqrt{8}\]

\[ =\] \[\times 2\sqrt{2}\]

 =

Line l touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following. 
(1) What is d(O, P) = ? Why ?
(2) If d(O, Q) = 8 cm, where does the point Q lie ?
(3) If d(OQ) = 15 cm, How many locations of point Q are line on line l? At what distance will each of them be from point P?

In the given fig, bisectors of ∠B and ∠C of ∆ABC intersect each other in point X. Line AX intersects side BC in point Y. AB = 5, AC = 4, BC = 6 then find `"AX"/"XY"`.

Draw a circle with radius 4.1 cm. Construct tangents to the circle from a point at a distance 7.3 cm from the centre.

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

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy [Use π =22/7]

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre

In ∆ABC, B - D - C and BD = 7, BC = 20 then Find following ratio. 

`"A(∆ ABD)"/"A(∆ ADC)"`

In the given fig, XY || seg AC. If 2AX = 3BX and XY = 9. Complete the activity to Find the value of AC.  

Activity : 2AX = 3BX  

∴ `"AX"/"BX" = square/square`

`"AX +BX"/"BX" = (square + square)/square` ...(by componendo)

`"AB"/"BX" = square/square`                  ...(I)

ΔBCA ~ ΔBYX                 ... `square` test of similarity,

∴ `"BA"/"BX" = "AC"/"XY"`  ...(corresponding sides of similar triangles)

∴ `square/square = "AC"/9`      

∴ AC = `square`        ...[From(I)]

In the given figure, point T is in the interior of rectangle PQRS, Prove that, TS² + TQ² = TP² + TR² (As shown in the figure, draw seg AB || side SR and A-T-B)

In the given figure, A is the centre of the circle. ∠ABC = 45^° and AC = 7√2 cm. Find the area of segment BXC.