Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Circles

Multiple Choice Questions

311. A line intersecting a circle in two points is called a ___________.

Diameter
Chord
Secant
Secant

118 Views

Short Answer Type

312. In the given Fig. 10.98, a circle is inscribed in a triangle A B C having side BC = 8 cm, AC = 10 cm and AB = 12 cm. Find AD, BE and CF.

247 Views

313. ΔABC is inscribed in a circle. Find the length BC.

92 Views

314. A point A is 13 cm from the centre of the circle. The length of the tangent drawn from A to the circle is 12 cm. Find the radius, of the circle.

88 Views

315. In figure, if ∠ATO = 40°, find ∠AOB.

105 Views

316.

In Fig. , PQ is tangent at point C to a circle with centre O. If AB is a diameter and ∠CAB = 30°, find ∠PCA.

30599 Views

317.

In Fig.2, a quadrilateral ABCD is drawn to circumscribe a circle, with centre O, in such a way that the sides AB, BC, CD and DA touch the circle at the points P, Q, R and S respectively. Prove that AB + CD = BC + DA.

2810 Views

318.

In Fig, from an external point P, two tangents PT and PS are drawn to a circle with centre O and radius r. If OP=2r, show that ∠ OTS = ∠ OST = 30°.

7763 Views

319.
In Fig. , O is the centre of a circle such that diameter AB = 13 cm and AC = 12 cm. BC is joined. Find the area of the shaded region. (Take π = 3.14)

In the given figure,

Given,
Diameter, AB= 13 cm
therefore,

Radius of the circle, r =13/2 = 6.5 cm
$angle space ACB space is space the space angle space in space the space semi minus circle. therefore space angle ACB space equals space 90 degree Now comma space in space increment ACB comma space using space Phythagoras space theorem comma space we space have AB squared space equals space AC squared plus BC squared left parenthesis 13 right parenthesis squared space equals space left parenthesis 12 right parenthesis squared plus left parenthesis BC right parenthesis squared left parenthesis BC right parenthesis squared space equals space left parenthesis 13 right parenthesis squared minus left parenthesis 12 right parenthesis squared space equals space 169 minus 144 space equals space 25 therefore comma BC space equals space square root of 25 space equals space 5 Now comma space area space of space shaded space region space equals space Area space of space semi space circle space minus Area space of space increment ACB equals 1 half πr squared minus 1 half straight x space BC space straight x space AC equals 1 half space straight x space 3.14 straight x space left parenthesis 6.5 right parenthesis squared space minus 1 half space straight x space 5 space straight x space 12 equals 66.33 minus 30 equals 36.33 space cm squared Thuss comma space the space area space of space the space shaded space region space is space 36.33 space cm squared.$