Archives

In Figure, if OA = 5 cm, AB = 8 cm and OD is perpendicular to AB, then CD is equal to: (A) 2 cm (B) 3 cm (C) 4 cm (D) 5 cm

The correct answer is (A) 2 cm Solution Given: Radius of the circle = r = AO = 5 cm Length of chord AB = 8 cm Since the line drawn... View Article

AD is a diameter of a circle and AB is a chord. If AD = 34 cm, AB = 30 cm, the distance of AB from the centre of the circle is : (A) 17 cm (B) 15 cm (C) 4 cm (D) 8 cm

The correct answer is (D) 8 cm Solution Diameter of the circle = d = AD = 34 cm ∴ Radius of the circle = r = d/2 = AO = 17 cm Length... View Article

ABCD is a trapezium in which AB || DC, DC = 30 cm and AB = 50 cm. If X and Y are, respectively the mid-points of AD and BC, prove that ar (DCYX) = 7/9 ar (XYBA)

Solution: Given According to the given details ABCD is a trapezium with AB || DC To prove: ar (DCYX) = 7/9 ar (XYBA) Construction Join... View Article

In Figure CD || AE and CY || BA. Prove that ar (CBX) = ar (AXY).

Solution: Given According to the given details CD||AE and CY || BA To prove: ar (ΔCBX) = ar (ΔAXY) . Proof Triangles on the... View Article

The medians BE and CF of a triangle ABC intersect at G. Prove that the area of △ GBC = area of the quadrilateral AFGE.

Solution: Given According to the given details BE & CF are medians E is the midpoint of AC F is the midpoint of AB To prove: area of... View Article

The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to intersect AD at P and BC at Q. Show that PQ divides the parallelogram into two parts of equal area.

Solution: Given According to the given details The diagonals of a parallelogram ABCD intersect at a point O. Through O, a line is drawn to... View Article

A point E is taken on the side BC of a parallelogram ABCD. AE and DC are produced to meet at F. Prove that ar (ADF) = ar (ABFC)

Solution: Given According to the given details ABCD is a parallelogram. E is a point on BC. AE and DC are produced to meet at F. To... View Article

In △ ABC, D is the mid-point of AB and P is any point on BC. If CQ || PD meets AB in Q (Figure), then prove that ar (BPQ) = 1/2 ar (ABC).

Solution: According to the given details We have the diagram as follows Given In △ ABC, D is the mid-point of AB P is any point on BC.... View Article

The area of the parallelogram ABCD is 90 cm2 (see Figure). Find (i) ar (ABEF) (ii) ar (ABD) (iii) ar (BEF)

Solution According to the given details Area of parallelogram, ABCD = 90 cm2 (i) We know that, Parallelograms on the same base and... View Article

X and Y are points on the side LN of the triangle LMN such that LX = XY = YN. Through X, a line is drawn parallel to LM to meet MN at Z (See Figure). Prove that ar (LZY) = ar (MZYX)

Solution: Given According to the given details LX=XY=YN XZ II LM To Prove ar (LZY) = ar (MZYX) Proof ar(LZX)+(XZY)=ar(LZY)... View Article

In Figure PSDA is a parallelogram. Points Q and R are taken on PS such that PQ = QR = RS and PA || QB || RC. Prove that ar (PQE) = ar (CFD).

Solution: Given According to the given details PA║QB║RC║SD & PQ=QR=RS From the Equal intercept theorem, we know that if... View Article

PQRS is a rectangle inscribed in a quadrant of a circle of radius 13 cm. A is any point on PQ. If PS = 5 cm, then ar (PAS) = 30 cm2. Write True or False and justify your answer:

The correc answer is (C) Perimeter of ABCD > Perimeter of ABEM Solution From rectangle ABEM, AB = EM ------(eq.1) [sides of rectangle]... View Article

ABCD is a parallelogram and X is the mid-point of AB. If ar (AXCD) = 24 cm², then ar (ABC) = 24 cm². Write True or False and justify your answer:

The correc answer is (C) DC × DL Solution We know that Area of parallelogram = Base × Corresponding altitude = AB ×... View Article

In Figure parallelogram ABCD and rectangle ABEF are of equal area, then : (A) Perimeter of ABCD = Perimeter of ABEM (B) Perimeter of ABCD < Perimeter of ABEM (C) Perimeter of ABCD > Perimeter of ABEM (D) Perimeter of ABCD = 1/2 (Perimeter of ABEM)

The correc answer is (C) DC × DL Solution Explanation: Area of parallelogram = Base × Corresponding altitude = AB ×... View Article

In Figure the area of parallelogram ABCD is: (A) AB × BM (B) BC × BN (C) DC × DL (D) AD × DL

The correc answer is (D) a rhombus of area 24 cm2 Solution According to the given details Let ABCD be the rectangle. E is the... View Article

In which of the following figures (Figuere), you find two polygons on the same base and between the same parallels?

Solution: The correct answer is (D) Explanation: In diagram (D), the parallelograms, PQRA and BQRS are on the same base QR and... View Article

The median of a triangle divides it into two (A) triangles of equal area (B) congruent triangles (C) right triangles (D) isosceles triangles

The correct answer is (A) triangles of equal area Solution A median of a triangle is a line segment that joins a vertex to the mid-point... View Article

In Figure AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.

Solution: Given According to the given details AB || DE, AB = DE, AC || DF and AC = DF To Prove BC || EF and BC = EF Proof From... View Article

ABCD is a quadrilateral in which AB || DC and AD = BC. Prove that ∠A = ∠B and ∠C = ∠D.

Given ABCD is a quadrilateral in which AB || DC and AD = BC. To Prove ∠A = ∠B and ∠C = ∠D. Proof According to... View Article

P and Q are the mid-points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.

Given P and Q are the mid-points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R... View Article

M	T	W	T	F	S	S
		1	2	3	4	5
6	7	8	9	10	11	12
13	14	15	16	17	18	19
20	21	22	23	24	25	26
27	28	29	30