Circles Mathematics - Circles

If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D . if ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠IBC

In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BAC

In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BEC

In the given figure, AB = BC = CD and ∠ABC = 132° . Calcualte: ∠AED

If I is the incentre of triangle ABC and AI when produced meets the circumcircle of triangle ABC in point D. If ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠DBC

In the figure, ∠DBC = 58°. BD is a diameter of the circle. Calculate : ∠BDC

In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.

Find: ∠BED

In the given figure, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°.

Find: ∠AOB

In the figure, given alongside, CP bisects angle ACB. Show that DP bisects angle ADB.

If I is the incentre of triangle ABC and AI when produced meets the cicrumcircle of triangle ABC in points D. f ∠BAC = 66° and ∠ABC = 80°. Calculate : ∠BIC.

D and E are points on equal sides AB and AC of an isosceles triangle ABC such that AD = AE. Prove that the points B, C, E and D are concyclic.

ABCD is a cyclic quadrilateral of a circle with centre O such that AB is a diameter of this circle and the length of the chord CD is equal to the radius of the circle. If AD and BC produced meet at P, Show that APB = 60°

In the given circle with diameter AB, find the value of x.

In the given figure, ∠ACE = 43° and ∠CAF = 62° ; Find the values of a, b and c.

In the given figure, ABCD is a cyclic quadrilateral. AF is drawn parallel to CB and DA is produced to point E. if ∠ADC = 92°, ∠FAE = 20°; determine ∠BCD. Give reason in support of your answer.

The quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic. Prove it.

In the given figure, chord ED is parallel to diameter AC of the circle. Given ∠CBE = 65°, calculate ∠DEC.

Prove that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

In the given figure, ABC is a triangle in which ∠BAC = 30°. Show that BC is equal to the radius of the circumcircle of the triangle ABC, whose centre is O.