Geometry Mathematics 2 Set 1 2018-2019 SSC (English Medium) 10th Standard Board Exam Question Paper Solution

If ΔABC ~ ΔPQR  and ∠A = 60°, then ∠P = ?

In right angle ΔABC, if ∠B = 90°, AB = 6, BC = 8, then find AC.

Write the length of largest chord of a circle with radius 3.2 cm.

From the given number line, find d(A, B):

Find the value of sin 30° + cos 60°.

Find the area of a circle of radius 7 cm.

Draw seg AB of length 5.7 cm and bisect it.

In right-angled triangle PQR, if ∠P = 60°, ∠R = 30° and PR = 12, then find the values of PQ and QR. 

In a right circular cone, if the perpendicular height is 12 cm and the radius is 5 cm, then find its slant height.

Choose the correct alternative: 

ΔABC and ΔDEF are equilateral triangles. If ar(ΔABC): ar(ΔDEF) = 1 : 2 and AB = 4, then what is the length of DE?

`2sqrt 2`

4

8

`4sqrt 2`

Choose the correct alternative: 

Out of the following which is a Pythagorean triplet? 

(5, 12, 14) 

(3, 4, 2)

(8, 15, 17)

(5, 5, 2)

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

65°

130°

295°

230°

Choose the correct alternative:

1 + tan² θ = ?

Sin² θ

Sec² θ

Cosec² θ 

Cot² θ

Construct tangent to a circle with centre A and radius 3.4 cm at any point P on it.

Find slope of a line passing through the points A(3, 1) and B(5, 3). 

Find the surface area of a sphere of radius 3.5 cm.

In ΔABC, ray BD bisects ∠ABC.

If A – D – C, A – E – B and seg ED || side BC, then prove that:

`("AB")/("BC") = ("AE")/("EB")`

Proof : 

In ΔABC, ray BD bisects ∠ABC.

∴ `("AB")/("BC") = (......)/(......)`   ......(i) (By angle bisector theorem)

In ΔABC, seg DE || side BC

∴ `("AE")/("EB") = ("AD")/("DC")`   ....(ii) `square`

∴ `("AB")/square = square/("EB")`   [from (i) and (ii)]

Prove that, angles inscribed in the same arc are congruent. 

Given: ∠PQR and ∠PSR are inscribed in the same arc

Arc PXR is intercepted by the angles. 

To prove: ∠PQR ≅ ∠PSR 

Proof : 

m∠PQR = `1/2` m(arc PXR)    .......(i) `square`

m∠`square` = `1/2` m(arc PXR)   ......(ii) `square`

∴ m∠`square` = m∠PSR     .......[From (i) and (ii)]

∴ ∠PQR ≅  ∠PSR       ........(Angles equal in measure are congruent)  

How many solid cylinders of radius 6 cm and height 12 cm can be made by melting a solid sphere of radius 18 cm? 

Activity: Radius of the sphere, r = 18 cm

For cylinder, radius R = 6 cm, height H = 12 cm 

∴ Number of cylinders can be made =`"Volume of the sphere"/square`

`= (4/3 pir^3)/square`

`= (4/3 xx 18 xx 18 xx 18)/square`

= `square`

In right-angled ΔABC, BD ⊥ AC. If AD= 4, DC= 9, then find BD.

Verify whether the following points are collinear or not:

A(1, –3), B(2, –5), C(–4, 7). 

If sec θ = `25/7`, then find the value of tan θ.

In ΔPQR, seg PM is a median, PM = 9 and PQ² + PR²  = 290. Find the length of QR. 

In the given figure, O is the centre of the circle, ∠QPR = 70° and m(arc PYR) = 160°, then find the value of the following m(arc QXR).

In the given figure, O is centre of circle. ∠QPR = 70° and m(arc PYR) = 160°, then find the value of the following ∠QOR.

In the given figure, O is centre of circle, ∠QPR = 70° and m(arc PYR) = 160°, then find the value of the following ∠PQR.

Draw a circle with radius 4.2 cm. Construct tangents to the circle from a point at a distance of 7 cm from the centre.

When an observer at a distance of 12 m from a tree looks at the top of the tree, the angle of elevation is 60°. What is the height  of the tree?  `(sqrt 3 = 1.73)`

A circle with centre P is inscribed in the ∆ABC. Side AB, side BC, and side AC touch the circle at points L, M, and N respectively. The radius of the circle is r.

Prove that: A(ΔABC) = `1/2` (AB + BC + AC) × r

In ΔABC, ∠ACB = 90°. seg CD ⊥ side AB and seg CE is angle bisector of ∠ACB.

Prove that: `(AD)/(BD) = (AE^2)/(BE^2)`.

Show that the points (2, 0), (–2, 0), and (0, 2) are the vertices of a triangle. Also, a state with the reason for the type of triangle.

In the above figure, `square`XLMT is a rectangle. LM = 21 cm, XL = 10.5 cm. Diameter of the smaller semicircle is half the diameter of the larger semicircle. Find the area of non-shaded region.