SSC (Marathi Semi-English) 10th Standard Board Exam [इयत्ता १० वी] - Maharashtra State Board Important Questions for Geometry Mathematics 2

Prove that "Opposite angles of a cyclic quadrilateral are supplementary".

In the following figure, in ΔPQR, seg RS is the bisector of ∠PRQ. If PS = 6, SQ = 8, PR = 15, find QR.

In the following figure RP: PK= 3:2, then find the value of A(ΔTRP):A(ΔTPK).

If two circles with radii 8 cm and 3 cm, respectively, touch internally, then find the distance between their centers.

In the given figure, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠NMS.

Prove the following theorem:

Tangent segments drawn from an external point to the circle are congruent.

ΔSHR ~ ΔSVU. In ΔSHR, SH = 4.5 cm, HR = 5.2 cm, SR = 5.8 cm and `"SH"/("SV")=3/5`. Construct ΔSVU.

∆ABC ~ ∆LMN. In ∆ABC, AB = 5.5 cm, BC = 6 cm, CA = 4.5 cm. Construct ∆ABC and ∆LMN such that `"BC"/"MN" = 5/4`.

Find the slope of the line passing through the points A(2, 3) and B(4, 7).

Determine whether the points are collinear.

A(1, −3), B(2, −5), C(−4, 7)

A person standing on the bank of river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60°. When he moves 40 m away from the bank, he finds the angle of elevation to be 30°. Find the height of the tree and width of the river. `(sqrt 3=1.73)`

Using Euler’s formula, find V if E = 30, F = 12.

Find the diagonal of a square whose side is 10 cm.

In Fig. 3, AP and BP are tangents to a circle with centre O, such that AP = 5 cm and ∠APB = 60°. Find the length of chord AB.

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?

In the following figure seg AB ⊥ seg BC, seg DC ⊥ seg BC. If AB = 2 and DC = 3, find `(A(triangleABC))/(A(triangleDCB))`

Prove that the angle bisector of a triangle divides the side opposite to the angle in the ratio of the remaining sides.

In the following figure, seg BE ⊥ seg AB and seg BA ⊥ seg AD. If BE = 6 and \[\text{AD} = 9 \text{ find} \frac{A\left( \Delta ABE \right)}{A\left( \Delta BAD \right)} \cdot\]

In the given figure, AD is the bisector of the exterior ∠A of ∆ABC. Seg AD intersects the side BC produced in D. Prove that :

\[\frac{BD}{CD} = \frac{AB}{AC}\]

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