Maharashtra Board Class 10 Maths Part 2 Geometry Important Questions 2027 (Repeated in Board Exams)

The ratio of corresponding sides of similar triangles is 3 : 5, then find the ratio of their areas.

In the given figure, seg XY parallel side AC. If 2AX = 3BX and XY = 9, complete the activity to find the value of AC. Activity: 2AX = 3BX; AX/BX = 3/2; (AX + BX)/BX = (3 + 2)/2; AB/BX = 5/2; triangle BCA ~ triangle BYX (AA test of similarity); BA/BX = AC/XY (corresponding sides); 5/2 = AC/9; AC = 22.5.

In the given figure, in triangle ABC ray BD bisects angle ABC, A - D - C, seg ED perpendicular to side BC, A - E - B, then to prove that AB/AE = BC/EB complete the activity. Activity: In triangle ABC, ray BD bisects angle B, AB/BC = AD/DC (I) (Angle bisector theorem); In triangle ABC, seg ED parallel side BC, AE/EB = AD/DC (II); from (I) and (II) AB/AE = BC/EB.

In the given figure angle MNP = 90 degrees, seg NQ perpendicular to seg MP, MQ = 9, QP = 4, find NQ.

If triangle ABC ~ triangle DEF, m angle B = 60 degrees, then m angle E = ................. (A) 30 degrees (B) 60 degrees (C) 90 degrees (D) 45 degrees

Out of the following which is a Pythagorean triplet? (a) (1, 5, 10) (b) (5, 12, 13) (c) (2, 3, 4) (d) (5, 5, 2)

Find the diagonal of a square whose side is 5 cm.

Find the side of a square if its diagonal is 10 root 2 cm.

Find the length of diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.

Two circles having radii 4 cm and 5 cm touch each other internally. Then the distance between the centres is ..................... (A) 4 cm (B) 5 cm (C) 1 cm (D) 9 cm

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

Prove that, opposite angles of a cyclic quadrilateral are supplementary.

In the given figure, seg PS is a tangent segment, line PR is a secant. If PQ = 3.6, QR = 6.4, find PS. Activity: PS² = PQ x PR (Tangent secant segment theorem) = PQ x [PQ + QR] = 3.6 x [3.6 + 6.4] = 3.6 x 10; PS² = 36; PS = 6.

Prove that: The tangent segments drawn from an external point to the circle are congruent.

AB is a chord of a circle with centre O. AC is a diameter of the circle. Line AT is a tangent at A. Write the answers: (a) Draw the figure using the given information. (b) Find the measure of angle CAT. (c) Find the measure of angle ABC.

angle ACB is inscribed angle in a circle with centre O. If angle ACB = 65 degrees, then what is measure of its intercepted arc AXB? (A) 65 degrees (B) 230 degrees (C) 295 degrees (D) 130 degrees

In the given figure, m(arc NS) = 125 degrees, m(arc EF) = 37 degrees. Find m angle NMS (angle formed by two secants meeting outside the circle).

In the given figure, chord EN and chord FS intersect each other at point M in the exterior of the circle. If m(arc NS) = 125 degrees, m(arc EF) = 37 degrees, then complete the activity to find angle NMS. Activity: m angle NMS = 1/2 [m(arc NS) - m(arc EF)] = 1/2 [125 - 37] = 1/2 (88) = 44 degrees.

triangle ABC ~ triangle ADE. In triangle ABC, AB = 6.3 cm, angle CAB = 50 degrees, AC = 5.6 cm and AB/AD = 7/5. Construct triangle ADE.

Draw a circle with centre O and radius 3.5 cm, take a point P at a distance 5.7 cm from the centre. Draw tangents to the circle from point P.

Draw a circle with centre O of radius 3.4 cm. Draw a chord MN of length 5.7 cm in it. Construct tangents at point M and N to the circle.

Angle made by the line with the positive direction of X-axis is 30 degrees. Find slope of the line.

If P is the midpoint of segment joining the points A(-4, 2) and B(6, 2), then complete the activity to find the co-ordinates of point P. Activity: (x1, y1) = (-4, 2), (x2, y2) = (6, 2); by midpoint formula x = (x1 + x2)/2 = 2/2 = 1, y = (y1 + y2)/2 = 4/2 = 2; co-ordinates of midpoint are (1, 2).

Find the co-ordinates of point P, if P divides the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 2 : 3.

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

Find the distance between the points P(-1, 1) and Q(5, -7).

Verify, whether points A(1, -3), B(2, -5) and C(-4, 7) are collinear or not.

Show that points P(-2, 3), Q(1, 2), R(4, 1) are collinear.

Seg AB is parallel to Y-axis and co-ordinates of point A are (1, 3), then the co-ordinates of point B are ........................ (A) (3, 1) (B) (5, 3) (C) (3, 0) (D) (1, -3)

A person is standing at a distance of 80 m from a Church looking at its top. The angle of elevation is 45 degrees. Find the height of the Church.

If sin theta = 20/29, then complete the activity to find cos theta. Activity: sin² theta + cos² theta = 1; cos² theta = 1 - sin² theta; cos² theta = 1 - 400/841; cos² theta = 441/841; taking square roots, cos theta = 21/29.

If sec theta = 25/7, find the value of tan theta. Solution: 1 + tan² theta = sec² theta; 1 + tan² theta = (25/7)²; tan² theta = 625/49 - 49/49 = 576/49; tan theta = 24/7.

Show that cot theta + tan theta = cosec theta x sec theta. Solution: L.H.S. = cot theta + tan theta = cos theta/sin theta + sin theta/cos theta = (cos² theta + sin² theta)/(sin theta x cos theta) = 1/(sin theta x cos theta) = 1/sin theta x 1/cos theta = cosec theta x sec theta = R.H.S.

If the side of the cube is 5 cm, then the volume of that cube is ..................................... (A) 10 cm3 (B) 100 cm3 (C) 125 cm3 (D) 25 cm3

Find surface area of a sphere of radius 7 cm.

Radius of a sector of a circle is 35 cm and length of its arc is 22 cm. What is the area of the sector? (a) 285 cm2 (b) 185 cm2 (c) 385 cm2 (d) 85 cm2

Find the number of coins of 2.2 cm diameter and 0.2 cm thick, that can be made by melting a metallic right circular cylinder of height 0.2 m and diameter 8.8 cm.

If radius of cone is 5 cm and its perpendicular height is 12 cm, then the slant height is ..................... . (A) 17 cm (B) 4 cm (C) 13 cm (D) 60 cm