SSC (English Medium) १० वीं कक्षा - Maharashtra State Board Question Bank Solutions for Geometry Mathematics 2

In ▢ABCD, seg AD || seg BC. Diagonal AC and diagonal BD intersect each other in point P. Then show that `"AP"/"PD" = "PC"/"BP"`.

The radii of the ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its curved surface area.

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its total surface area.

The radii of ends of a frustum are 14 cm and 6 cm respectively and its height is 6 cm. Find its volume \[\pi\] = 3.14) 

The circumferences of circular faces of a frustum are 132 cm and 88 cm and its height is 24 cm. To find the curved surface area of the frustum complete the following activity.( \[\pi = \frac{22}{7}\]) 

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.

A washing tub in the shape of a frustum of a cone has a height of 21 cm. The radii of the circular top and bottom are 20 cm and 15 cm respectively. What is the capacity of the tub? ( \[\pi = \frac{22}{7}\]).

In the figure Q is the contact point. If
PQ = 12, PR = 8, then PS = ?

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.

In Δ ABC and Δ PQR,
∠ ABC ≅ ∠ PQR, seg BD and
seg QS are angle bisector.
`If  (l(AD))/(l(PS)) = (l(DC))/(l(SR))`
Prove that : Δ ABC ∼ Δ PQR

Seg NQ is the bisector of ∠ N
of Δ MNP. If MN= 5, PN =7,
MQ = 2.5 then find QP.

From the top of a light house, an abserver looking at a boat makes an angle of depression of 600. If the height of the lighthouse is 90 m then find how far is the boat from the lighthouse. (3 = 1.73)

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)]

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

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

In the figure, ray YM is the bisector of ∠XYZ, where seg XY ≅ seg YZ, find the relation between XM and MZ. 

Δ AMT ∼ ΔAHE. In  Δ AMT, MA = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `(MA)/(HA) = 7/5`. construct  Δ AHE. 

Draw seg AB = 6.8 cm and draw perpendicular bisector of it. 

Find the co-ordinates of the centroid of the Δ PQR, whose vertices are P(3, –5), Q(4, 3) and R(11, –4)