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

Solve sub-questions:

If two circles with diameters 8 cm and 6 cm respectively touch externally, find the distance between their centers.

Solve sub-questions:

In the following figure, seg AB is a diameter of the circle, m (arc AKC) = 40° . Find the value of m (arc BMC).

Solve Question:

In the following figure, if m(arc DXE) = 100° and m(arc AYC) = 40°, find ∠DBE.

Solve any three sub-questions:

In the following figure, secants containing chords RS and PQ of a circle intersects each other in point A in the exterior of a circle. If m(arc PCR) = 26°, m(arc QDS) = 48°, then find:

(i) m∠PQR

(ii) m∠SPQ

(iii) m∠RAQ

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?

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).

Four alternative answers for each of the following questions are given. Choose the correct alternative.

Two circles intersect each other such that each circle passes through the centre of the other. If the distance between their centres is 12, what is the radius of each circle?

In figure 3.90, seg AB is a diameter of a circle with centre C. Line PQ is a tangent, which touches the circle at point T. seg AP line PQ and seg BQ line PQ. Prove that, seg CP ≅seg CQ.

In figure 3.98, seg AB is a diameter of a circle with centre O . The bisector of∠ ACB intersects the circle at point D. Prove that, seg AD ≅seg BD.

Complete the following proof by filling in the blanks.

Proof: Draw seg OD.

…90° ............ angle inscribed in semicircle

........45° .... CD is the bisector of

m(arc DB) = ........45° .. inscribed angle theorem

…............90° definition of measure of an arc (I)

seg OA ≅seg OB .......radii of the circle... (II)

∴line OD is of seg AB ......bisector.... From (I) and (II)

∴seg AD ≅seg BD

In figure 3.86, circle with centre M touches the circle with centre N at point T. Radius RM touches the smaller circle at S. Radii of circles are 9 cm and 2.5 cm. Find the answers to the following questions hence find the ratio MS:SR.

(1) Find the length of segment MT

(2) Find the length of seg MN

(3) Find the measure of ∠ NSM.