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- Arc and Chord Properties - Angles in the Same Segment of a Circle Are Equal (Without Proof)
A triangle ABC is inscribed in a circle. The bisectors of angles BAC, ABC and ACB meet the circumcircle of the triangle at points P, Q and R respectively. Prove that :
(i) ∠ABC = 2∠APQ,
(ii) ∠ACB = 2∠APR,
(iii) ∠QPR = 90 -`1/2` ∠BAC
The given figure shows a circle with centre O and ∠ABP = 42°
Calculate the measure of:
(ii) ∠QPB + ∠PBQ
If two sides of a cyclic quadrilateral are parallel; prove that:
(i) its other two sides are equal.
(ii) its diagonals are equal.
In the figure, given below, AD = BC, ∠BAC = 30° and ∠CBD = 70°.
Find: (i) ∠BCD (ii) ∠BCA (iii) ∠ABC (iv) ∠ADB
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 :
(i) ∠DBC (ii) ∠IBC (iii) BIC
In the figure, ∠BAD = 65° , ∠ABD = 70° , ∠BDC = 45°
(i) Prove that AC is a diameter of the circle
(ii) Find ∠ACB