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
- If the distance of a variable point \(P\) from a point \(A(2,-2)\) is twice the distance of \(P\) from the Y-axis, then the equation of locus of \(P\) is:
- The coordinate axes are rotated about the origin in the counterclockwise direction through an angle \( 60^\circ \). If \( a \) and \( b \) are the intercepts made on the new axes by a straight line whose equation referred to the original axes is \( x + y = 1 \), then \( \dfrac{1}{a^2} + \dfrac{1}{b^2} = \, ? \)
- The image of a point \( (2, -1) \) with respect to the line \( x - y + 1 = 0 \) is
- If \( \sinh^{-1}(2) + \sinh^{-1}(3) = \alpha \), then \( \sinh\alpha = \) ?
- If in \( \triangle ABC \), \( B = 45^\circ \), \( a = 2(\sqrt{3} + 1) \) and area of \( \triangle ABC \) is \( 6 + 2\sqrt{3} \) sq. units, then the side \( b = \ ? \)
View More Questions
Questions Asked in CAT exam
- When Rajesh's age was same as the present age of Garima, the ratio of their ages was 3 : 2. When Garima's age becomes the same as the present age of Rajesh, the ratio of the ages of Rajesh and Garima will become
- CAT - 2024
- Ratio and Proportion
- Two points A and B are 45 km apart. Anil started from A. Sunil started from B. They met each other after 1 hour 30 mins. and after meeting, they continued towards their destinations. Time taken by Anil to reach Point B was 1 hr 15 mins more than the time taken by Sunil to reach point A. Find speed of Anil
- CAT - 2024
- Time, Speed and Distance
- The sum of all four-digit numbers that can be formed with the distinct non-zero digits $a$, $b$, $c$, and $d$, with each digit appearing exactly once in every number, is $153310 + n$, where $n$ is a single digit natural number. Then, the value of $(a + b + c + d)$ is ?
- CAT - 2024
- Permutations and Combinations
- The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
- CAT - 2024
- Profit and Loss
- In the $XY$-plane, the area, in sq. units, of the region defined by the inequalities $y \ge x + 4$ and $-4 \le x^2 + y^2 + 4(x - y) \le 0$ is
- CAT - 2024
- Coordinate Geometry
View More Questions