In a circle of radius 21 cm, an arc subtends an angle of $60°$ at the centre.Find: (i) the length of the arc (ii) area of the sector formed by the arc.
 $\left| \mathrm{Use} \mathrm{\pi } = \frac{22}{7 }\right|$

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, $\angle$B = 90^o and DS = 5 cm, then the radius of thecircle (in cm) is 

• 11

• 18

• 6

• 15

In fig., PA and PB are two tangents drawn from an external point P to a circlewith centre C and radius 4 cm. If PA PB, then the length of each tangent is

• 3

• 4

• 5

• 6

Prove that the parallelogram circumscribing a circle is a rhombus.

Two circular pieces of equal radii and maximum area, touching each otherare cut out from a rectangular card board of dimensions 14 cm x 7 cm. Find the area of the remaining card board.

[ Use π = 22/7 ]

In fig., a circle is inscribed in triangle ABC touches its sides AB, BC and ACat points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10cm, then find the length of AD, BE and CF.

In fig., l and m are two parallel tangents to a circle with centre O,touching the circle at A and B respectively. Another tangent at C intersects the line l at D and m at E. Prove that   $\angle$DOE = 90⁰

Prove that the tangent at any point of a circle is perpendicular to theradius through the point of contact.

Two circles touch each other externally at P. AB is a common tangent to the circlestouching them at A and B. The value of ∠APB is

• 30°

• 45°

• 60°

• 90°

A chord of a circle of radius 10 cm subtends a right angleat its centre. The length of the chord (in cm) is

• 5$\sqrt{2}$

• 10$\sqrt{2}$

• $\frac{5}{\sqrt{2}}$

• 10$\sqrt{3}$