P-2 Circle Maths - P-2 Circle

Four alternative answers for each of the following questions are given. Choose the correct alternative.
Points A, B, C are on a circle, such that m(arc AB) = m(arc BC) = 120°. Nopoint, except point B, is common to the arcs. Which is the type of ∆ ABC?
A. Equilateral triangle
B. Scalene triangle
C. Right angled triangle
D. Isosceles triangle

Four alternative answers for each of the following questions are given. Choose the correct alternative.
Chords AB and CD of a circle intersect inside the circle at point E. If AE = 5.6,EB = 10, CE = 8, find ED.
A. 7
B. 8
C. 11.2
D. 9

Four alternative answers for each of the following questions are given. Choose the correct alternative.
∠ ACB is inscribed in arc ACB of a circle with centre O. If ∠ ACB = 65°,find m(arc ACB).
A. 65°
B. 130°
C. 295°
D. 230°

Four alternative answers for each of the following questions are given. Choose the correct alternative.
If two circles are touching externally, how many common tangents of them can be drawn?
A. One
B. Two
C. Three
D. Four

prove the theorem Opposite angles of a cyclic quadrilateral are supplementry.

In figure 3.80, if PQ = 6, QR = 10, PS = 8 find TS.

In figure 3.78, chord MN and chord RS intersect at point D.
(1) If RD = 15, DS = 4, MD = 8 find DN
(2) If RS = 18, MD = 9, DN = 8 find DS

In figure 3.77, ray PQ touches the circle at point Q. PQ = 12, PR = 8, find PS and RS.

In figure 3.61, chords AC and DE intersect at B. If ∠ ABE = 108°, m(arc AE) = 95°, find m(arc DC).

In figure 3.60, m(arc NS) = 125°, m(arc EF) = 37°, find the measure ∠ NMS.

Prove that, any rectangle is a cyclic quadrilateral.

In fig 3.39 chord AB ≅ chord CD, Prove that, arc AC ≅ arc BD

In figure 3.58, seg RS is a diameter of the circle with centre O. Point T lies in the exterior of the circle. Prove that ∠ RTS is an acute angle.

In figure 3.56, in a circle with centre O, length of chord AB is equal to the radius of the circle. Find measure of each of the following.

(1) ∠ AOB (2) ∠ ACB
(3) arc AB (4) arc ACB.

Two circles of radii 5.5 cm and 4.2 cm touch each other externally. Find the distance between their centres.

Two circles having radii 3.5 cm and 4.8 cm touch each other internally. Find the distance between their centres.

What is the distance between two parallel tangents of a circle having radius4.5 cm ? Justify your answer.

Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON.

In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then
What is the measure of ∠MRN?