Question:
∆ABC is inscribed inside a circle and there is a point D on the arc BC opposite to A such that BD = CD. If ∠BAC = 70° and ∠ABD = 85°, then find the measure of ∠BCA.
∆ABC is inscribed inside a circle and there is a point D on the arc BC opposite to A such that BD = CD. If ∠BAC = 70° and ∠ABD = 85°, then find the measure of ∠BCA.
Updated On: Sep 10, 2024
- 45°
- 55°
- 35°
- 60°
Hide Solution
Verified By Collegedunia
The Correct Option is D
Solution and Explanation
The correct option is (D): 60°
The opposite angles in a cyclic quadrilateral are supplementary.
∠BAC + ∠BDC = 180°
∠ABD + ∠ACD = 180°
∠BDC = 110°
∠ACD = 95°
In ∆BCD:
∠BCD = ∠CBD [BD = CD]
∠BCD + ∠CBD + ∠BDC = 180°
∠BCD = 35°
∠ACD = 95°
∠BCA + ∠BCD = 95°
∠BCA = 60°
The opposite angles in a cyclic quadrilateral are supplementary.
∠BAC + ∠BDC = 180°
∠ABD + ∠ACD = 180°
∠BDC = 110°
∠ACD = 95°
In ∆BCD:
∠BCD = ∠CBD [BD = CD]
∠BCD + ∠CBD + ∠BDC = 180°
∠BCD = 35°
∠ACD = 95°
∠BCA + ∠BCD = 95°
∠BCA = 60°
Was this answer helpful?
0
0
Top Questions on Triangles
- In \( \triangle ABC \), if \( r_1 = 4 \), \( r_2 = 8 \), \( r_3 = 24 \), then find \( a \)=
- In \( \triangle ABC \), if \( a = 13 \), \( b = 14 \), and \( \cos \frac{C}{2} = \frac{3}{\sqrt{13}} \), then \( 2r_1 = \):
- If 7 and 8 are the lengths of two sides of a triangle and \( a \) is the length of its smallest side. The angles of the triangle are in AP and \( a \) has two values \( a_1 \) and \( a_2 \) satisfying this condition. If \( a_1 < a_2 \), then \( 2a_1 + 3a_2 = \):
- In \( \triangle ABC \), if \( (r_2 - r_1)(r_3 - r_1) = 2r_2r_3 \), then \( 2(r + R) = \):
- If the orthocentre of the triangle formed by the lines 2x + 3y – 1 = 0, x + 2y – 1 = 0 and ax + by – 1 = 0, is the centroid of another triangle, whose circumecentre and orthocentre respectively are (3, 4) and (–6, –8), then the value of |a– b| is_____.
View More Questions
Questions Asked in CAT exam
- For any natural Number 'n', let an be the largest number not exceeding \(\sqrt{n}\) , then a1 + a2 + a3... +a50 =
- CAT - 2024
- Number Systems
- The number of all positive integers up to 500 with non-repeating digits is
- CAT - 2024
- Number Systems
- The sum of all real values of $k$ for which $(\frac{1}{8})^k \times (\frac{1}{32768})^{\frac{4}{3}} = \frac{1}{8} \times (\frac{1}{32768})^{\frac{k}{3}}$ is
- CAT - 2024
- Logarithms
- When $10^{100}$ is divided by 7, the remainder is ?
- CAT - 2024
- Basics of Numbers
- In September, the incomes of \(K\), \(A\), and \(V\) are in the ratio \(8:6:5\). They rent a house, contributing \(15\%\), \(12\%\), and \(18\%\) of their respective incomes. In October, the rent remains the same, but the salaries of \(K\), \(A\), and \(V\) increase by \(10\%\), \(12\%\), and \(15\%\), respectively. What percentage of their total income is paid as house rent in October? (Round to the nearest percentage.)
- CAT - 2024
- Percentages
View More Questions