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A, B and C are three points on a circle. Prove that the perpendicular bisectors of AB, BC and CA are concurrent.

Given According to the given details Three non-collinear points A, B and C are on a circle. To Prove We have to prove that perpendicular... View Article

f the perpendicular bisector of a chord AB of a circle PXAQBY intersects the circle at P and Q, prove that arc PXA ≅ Arc PYB

Given According to the given details PQ is the perpendicular bisect of AB, To Prove We have to prove that arc PXA ≅ Arc PYB Solution... View Article

If arcs AXB and CYD of a circle are congruent, find the ratio of AB and CD.

Given According to the given details AXB ≅ CYD Find out We have to determine the ratio of AB and CD. Solution We know that,... View Article

A circle of radius 3 cm can be drawn through two points A, B such that AB = 6 cm. Write True or False and justify your answer in each of the following:

The given statement is True Explanation According to the given details Radius of circle = 3 cm Diameter of circle = 2 × r = 2... View Article

Through three collinear points a circle can be drawn. Write True or False and justify your answer in each of the following:

The given statement is False Explanation A circle through two points cannot pass through a point that is collinear to these two... View Article

Two congruent circles with centres O and O’ intersect at two points A and B. Then ∠AOB = ∠AO’B. Write True or False and justify your answer in each of the following:

The given statement is True Explanation Equal chords of congruent circles subtend equal angles at the respective centre. Let us consider... View Article

Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC . Write True or False and justify your answer in each of the following:

The given statement is False Explanation Let AB and AC be the chord of the circle with centre O on the opposite side of OA.... View Article

Two chords AB and CD of a circle are each at distances 4 cm from the centre. Then AB = CD. Write True or False and justify your answer in each of the following:

The given statement is True Explanation Given that AB and AC are chords that are at a distance of 4 cm from the centre of a circle. Since,... View Article

In Figure if AOB is a diameter of the circle and AC = BC, then ∠CAB is equal to: (A) 30º (B) 60º (C) 90º (D) 45º

The correct answer is (D) 45º Solution According to the given details Diameter of the circle = AOB AC = BC Since, angles... View Article

In Figure if ∠ABC = 20º, then ∠AOC is equal to: (A) 20º (B) 40º (C) 60º (D) 10º

The correct answer is (B) 40º Solution According to the given details ∠ABC = 20° According to the theorem, we know that,... View Article

If AB = 12 cm, BC = 16 cm and AB is perpendicular to BC, then the radius of the circle passing through the points A, B and C is : (A) 6 cm (B) 8 cm (C) 10 cm (D) 12 cm

The correct answer is (C) 10 cm Solution According to the given details AB = 12 cm, BC = 16 cm, AB ⊥ BC. Hence AC is the... View Article

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

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