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If two equal chords of a circle intersect, prove that the parts of one chord are separately equal to the parts of the other chord.

Given According to the given details AB and CD are two equal chords of a circle with centre O, intersect each... View Article

If BM and CN are the perpendiculars drawn on the sides AC and AB of the triangle ABC, prove that the points B, C, M and N are concyclic.

Given According to the given details BM and CN are the perpendiculars drawn on the sides AC and AB of the... View Article

Two chords AB and AC of a circle subtends angles equal to 90º and 150º, respectively at the centre. Find ∠BAC, if AB and AC lie on the opposite sides of the centre.

Given According to the given details ∠AOC=90º and∠AOB= 150º Find out We have to determine ∠BAC, Solution In ΔAOB, OA = OB (radius... View Article

On a common hypotenuse AB, two right triangles ACB and ADB are situated on opposite sides. Prove that ∠BAC = ∠BDC.

Given According to the given details ACB and ADB are two right triangles. To Prove We have to prove that ∠BAC... View Article

O is the circumcentre of the triangle ABC and D is the mid-point of the base BC. Prove that ∠BOD = ∠A.

Given According to the given details O is the circumcenter of the triangle ABC and D is the midpoint of BC.... View Article

ABCD is such a quadrilateral that A is the centre of the circle passing through B, C and D. Prove that ∠CBD + ∠CDB = 1/2 ∠BAD

Given According to the given details A quadrilateral ABCD such that A is the centre of the circle passing through B,... View Article

If a line segment joining mid-points of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Given According to the given details AB and CD to be the chords of the circle with centre O. To Prove... View Article

AB and AC are two equal chords of a circle. Prove that the bisector of the angle BAC passes through the centre of the circle.

Given According to the given details AB and AC are two chords that are equal with centre O. AM is the... View Article

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... 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... 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... 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 =... 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... 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... 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... 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... 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... 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,... 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... View Article

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