In ΔABC, ∠A = 48°. AB and AC is extended to points D and E respectively, if the bisectors of angle CBD and angle BCE meet at point O, then ∠BOC is equal to:
66°
The correct answer is 66°.
For a triangle ABC, if the exterior angle bisectors of $\angle\text{B}$ and $\angle\text{C}$ meet at O, then the relationship is: $\angle\text{BOC} = 90^\circ - \frac{1}{2}\angle\text{A}$ This theorem provides a shortcut for problems like this one, directly relating the angle at O to the opposite interior angle $\angle\text{A}$. Similarly, if interior angle bisectors of $\angle\text{B}$ and $\angle\text{C}$ meet at a point I, then $\angle\text{BIC} = 90^\circ + \frac{1}{2}\angle\text{A}$. It is important not to confuse these two theorems.
Similar Questions
G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
In a triangle, if the angles are in the ratio 1 ∶ 2 ∶ 3, then the ratio of the corresponding sides is:
Given that Δ MAN and Δ CPT are congruent to each other such that ∠M = 75, ∠N = 65, ∠A = 40, ∠C = x/2, ∠P = 6y + 16. Find the value of (x – 5y).
If M is the mid-point of the side BC of ABC, and the area of ABM is 19 cm2 , then the area of ABC is:
In Δ PQR, S and T are points on the sides PQ and PR, respectively, such that Δ PST is similar to Δ PRQ. If m ∠PQR = 47°, then find m ∠STR.
It is given that ΔABC ∼ ΔYZX and Ar ΔABC : Ar ΔXYZ = 256 : 25. If AB = 12 cm, BC = 10 cm, CA = 15 cm, then what is the value of YZ (in cm)?
In trapezium ABCD, AB∥DC. The sides AD and BC are produced to meet at E. AB = 15 cm, CD = 10 cm, AD = 4 cm and BC = 5 cm, then DE = ?
In Δ ABC, ∠C = 70°. The bisectors of ∠A and<B meet BC and AC in points D and E, respectively. AD and BE intersect each other at P. What is the measure of ∠DPB?
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Important Questions from Triangles, Congruence and Similarity
G is the centroid of the equilateral triangle ABC. If AB = 8√ 3 cm, then the length of AG is equal to:
If sides of a triangle are 12 cm, 15 cm and 21 cm, then what is the inradius (in cm) of the triangle?
What is the area of quadrilateral ABCD?
It is given that ΔABC ~ ΔXYZ and Area ΔABC : Area ΔXYZ = 81 : 25. If AB = 18 cm, BC = 10 cm, CA = 15 cm, then what is the side XZ (in cm)?
Sides of two similar triangles are in the ratio 4 ∶ 9. Area of these triangles are in the ratio:
