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Syllabus

$\frac{arcAPB}{2}=\frac{{\displaystyle arcBQC}}{{\displaystyle 2}}=\frac{{\displaystyle arcCRA}}{{\displaystyle 2}}\phantom{\rule{0ex}{0ex}}Find\angle BOC.$

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(ICSE)Hint: Minor arc AB = minor arc CD. Subtract minor arc BD from both sides.

(i) AP = CP,

(ii) BP = DP

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Q.8. In the given figure, AB and CD are two equal chords of a circle, with centre O. If P is the mid-point of chord AB, Q is the mid-point of chord CD and $\angle POQ=150\xb0$, find $\angle APQ$.

Q3. Two points A and B are given. Find the set of feet of the perpendiculars dropped from the point A onto all possible straight lines passing through the point B.

32. To prove SQ = SR

SP is bisector of $\angle $RPT and PQRS is a cyclic quadrilateral.

10. In Fig.13.35, CD is the perpendicular bisector of the chord AB. If AB = 2 cm and CD = 4 cm, calculate the radius of the circle.

(SC)Q.1. A chord of length 16 cm is drawn in a circle of diameter 20 cm. Calculate its distance from the centre of the circle.

Q.3. The radius of a circle is 17.0 cm and the length of perpendicular drawn from its centre to a chord is 8.0 cm. Calculate the length of the chord.

19. (a) In the figure (i) given below, a line l intersects two concentric circles at the points A, B, C and D. Prove that AB = CD.

(b) In the figure (ii) given below, chords AB and CD of a circle with centre O intersect at E. If OE bisects $\angle AED$, prove that AB = CD.

10. ABC is an isosceles triangle inscribed in a circle. If AB=AC=$12\sqrt{5}$cm and BC=24 cm, find the radius of the circle.

13. A rectangle with one side of length 4 cm is inscribed in a circle of diameter 5 cm. Find he area of the rectangle.