Question:
Consider a square ABCD with midpoints E, F, G and H of sides AB, BC, CD and DA. Let L denote the line passing through F and H. Consider points P and Q on the line L inside the square such that the angles APD and BQC are both equal 120 degrees. What is the ratio ABQCDP to the remaining area of ABCD?
Consider a square ABCD with midpoints E, F, G and H of sides AB, BC, CD and DA. Let L denote the line passing through F and H. Consider points P and Q on the line L inside the square such that the angles APD and BQC are both equal 120 degrees. What is the ratio ABQCDP to the remaining area of ABCD?
Updated On: Jul 29, 2024
- \(\frac {4\sqrt 2}{3}\)
- \(2\sqrt 3-1\)
- \(2+\sqrt 3\)
- \(\frac {10-3\sqrt 3}{9}\)
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
The correct option is (B): \(2\sqrt 3-1\).
Was this answer helpful?
0
0
Top Questions on Geometry
- Consider a right-angled triangle ABC, right angled at B. Two circles, each of radius r, are drawn inside the triangle in such a way that one of them touches AB and BC, while the other one touches AC and BC. The two circles also touch each other (see the image below).
If AB = 18 cm and BC = 24 cm, then find the value of r.
- A group of boys is practising football in a rectangular ground. Raju and Ratan are standing at the two opposite mid-points of the two shorter sides. Raju has the ball, who passes it to Rivu, who is standing somewhere on one of the longer sides. Rivu holds the ball for 3 seconds and passes it to Ratan. Ratan holds the ball for 2 seconds and passes it back to Raju. The path of the ball from Raju to Rivu makes a right angle with the path of the ball from Rivu to Ratan. The speed of the ball, whenever passed, is always 10 metre per second, and the ball always moves on straight lines along the ground.
Consider the following two additional pieces of information:
I. The dimension of the ground is 80 metres × 50 metres.
II. The area of the triangle formed by Raju, Rivu and Ratan is 1000 square metres.
Consider the problem of computing the following: how many seconds does it take for Raju to get the ball back since he passed it to Rivu? Choose the correct option. - A farmer has a triangular plot of land. One side of the plot, henceforth called the base, is 300 feet long and the other two sides are equal. The perpendicular distance, from the corner of the plot, where the two equal sides meet, to the base, is 200 feet.
To counter the adverse effect of climate change, the farmer wants to dig a circular pond. He plans that half of the circular area will be inside the triangular plot and the other half will be outside, which he will purchase at the market rate from his neighbour. The diameter of the circular plot is entirely contained in the base and the circumference of the pond touches the two equal sides of the triangle from inside.
If the market rate per square feet of land is Rs. 1400, how much does the farmer must pay to buy the land from his neighbour for the pond? (Choose the closest option.) - A rectangle \(ABCD\) has sides \(AB = 45 \, \text{cm}\) and \(BC = 26 \, \text{cm}\). Point \(E\) is the midpoint of side \(CD\). Find the radius of the incircle of the triangle \(\triangle AED\).
- PQR is a triangle. The bisectors of the internal angle ∠Q and external angle ∠R intersect at M. If ∠QMR = 40°, then ∠P is:
View More Questions
Questions Asked in SNAP exam
- To select a group, an unbiased dice is rolled out. If the dice shows 1 then group x is chosen. If 2 or 3 is shown, group y is chosen and if 4, 5 or 6 is shown, group z is chosen. Group x has 3 girls and 2 boys, group y has 3 girls and 4 boys, and group z has 4 girls and 5 boys. The dice is rolled out and the group is chosen, if a girl is chosen then find the probability that is it chosen from group y.
- SNAP - 2023
- Probability
- Roy bought articles at Rs. 20 per item. He sells them for Rs. 4, Rs. 6. He intends to make a profit of at least 40%. What will be the min number of articles he should sell?
- SNAP - 2023
- Profit and Loss
- Imran sold a mobile phone for Rs. 17600 after a discount of 12%, he made a profit of 10%. If no discount is given, find the profit percentage.
- SNAP - 2023
- Percentage
- A & B work 5 hours a day and complete work in 2 days. B and C work 5 hours a day and complete the same work in 4 days. A and C work 6 hours a day and complete the same in 2 days. How many days will A take to complete the work if he is working 5 hours a day alone?
- SNAP - 2023
- Time and Work
View More Questions