Advertisements
Advertisements
Question
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
Solution
Join DB and DC , IB and IC ,
∠ BAC = 66° , ∠ ABC = 80° , I is the incentre of the Δ ABC,
Since I is the incentre of ∆ABC, IB bisects ∠ABC
∴ ∠ IBC = `1/2` ∠ABC = `1/2 xx 80° = 40° `
APPEARS IN
RELATED QUESTIONS
In the given figure, ∠BAD = 65°, ∠ABD = 70° and ∠BDC = 45°. Find:
- ∠BCD
- ∠ACB
Hence, show that AC is a diameter.
The given figure shows a circle with centre O and ∠ABP = 42°.
Calculate the measure of:
- ∠PQB
- ∠QPB + ∠PBQ
In a cyclic-trapezium, the non-parallel sides are equal and the diagonals are also equal. Prove it.
In the given figure, AB = AD = DC = PB and ∠DBC = x°. Determine, in terms of x :
- ∠ABD,
- ∠APB.
Hence or otherwise, prove that AP is parallel to DB.
In cyclic quadrilateral ABCD; AD = BC, ∠BAC = 30° and ∠CBD = 70°; find:
- ∠BCD
- ∠BCA
- ∠ABC
- ∠ADC
AB is a diameter of the circle APBR as shown in the figure. APQ and RBQ are straight lines. Find : ∠PBR
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 :
∠ACB = 2∠APR,
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.
In the following figure, O is the centre of the circle, ∠ PBA = 42°.
Calculate:
(i) ∠ APB
(ii) ∠PQB
(iii) ∠ AQB
In the figure, AB = AC = CD, ∠ADC = 38°. Calculate: (i) ∠ ABC, (ii) ∠ BEC.
