Geometry Mathematics 2 Shaalaa.com Model Set 4 2019-2020 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

In the given figure, seg XY || seg BC, then which of the following statements is true?

`"AB"/"AC" = "AX"/"AY"`

`"AX"/"XB" ="AY"/"AC"`

`"AX"/"YC" = "AY"/"XB"`

`"AB"/"YC" = "AC"/"XB"`

Select the correct alternative for the following question.

(3) If ∆ABC ~ ∆PQR and `(AB)/(PQ) = 7/5`, then ...............

∆ABC is bigger. 

∆PQR is bigger.

Both triangles will be equal.

Can not be decided. 

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

Altitude on the hypotenuse of a right angled triangle divides it in two parts of lengths 4 cm and 9 cm. Find the length of the altitude.

9 cm 

4 cm

6 cm  

\[2\sqrt{6}\] cm

∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).

65°

130°

295°

230°

In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find `("A"(∆"ABC"))/("A"(∆"ADB"))`

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

Determine whether the following point is collinear.

D(–2, –3), E(1, 0), F(2, 1)

Find the surface area and the volume of a beach ball shown in the figure. 

Are the triangles in the given figure similar? If yes, by which test? 

In ∆ABC, point M is the midpoint of side BC. If, AB² + AC² = 290 cm², AM = 8 cm, find BC.

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.

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

If \[\sin\theta = \frac{7}{25}\], find the values of cosθ and tan​θ.

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, a cylindrical wrapper of flat tablets is shown. The radius of a tablet is 7 mm and its thickness is 5 mm. How many such tablets are wrapped in the wrapper? 

If ∆ABC ~ ∆PQR, A (∆ABC) = 80, A (∆PQR) = 125, then fill in the blanks. \[\frac{A\left( ∆ ABC \right)}{A\left( ∆ . . . . \right)} = \frac{80}{125} \therefore \frac{AB}{PQ} = \frac{......}{......}\] 

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, the vertices of square DEFG are on the sides of ∆ABC. ∠A = 90°. Then prove that DE² = BD × EC. (Hint: Show that ∆GBD is similar to ∆CFE. Use GD = FE = DE.) 

Draw a circle with centre P. Draw an arc AB of 100° measure. Draw tangents to the circle at point A and point B.

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.

In a trapezium ABCD, seg AB || seg DC seg BD ⊥ seg AD, seg AC ⊥ seg BC, If AD = 15, BC = 15 and AB = 25. Find A(▢ABCD)

In the given figure, a ∆ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC are of lengths 8 cm and 6 cm respectively. Find the lengths of sides AB and AC, when area of ∆ABC is 84 cm². 

The difference between outer and inner curved surface areas of a hollow right circular cylinder 14cm long is 88cm². If the volume of metal used in making cylinder is 176cm³.find the outer and inner diameters of the cylinder____?

Prove that:

`"tanθ"/("secθ"  –  1) = (tanθ + secθ + 1)/(tanθ + secθ - 1)`

In the given figure, square ABCD is inscribed in the sector A - PCQ. The radius of sector C - BXD is 20 cm. Complete the following activity to find the area of shaded region