Concurrent Lines — Flashcards
NIOS · Class 10 · Maths
24 flashcards for Concurrent Lines (NIOS Class 10 Maths) to test yourself on key terms and facts. Sample: "In triangle ABC, AD, BE, and CF are angle"
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In triangle ABC, AD, BE, and CF are angle bisectors. What do you conclude?
Answer
Step 1: A triangle has three angles, so three angle bisectors can be drawn. Step 2: The three angle bisectors of a triangle are concurrent. Step 3: Their point of concurrency is called the incentre, I…
In triangle ABC, the angle bisectors meet at I. What key distance property does I have?
Answer
Step 1: A point on an angle bisector is equidistant from the two sides of the angle. Step 2: Since I lies on the angle bisectors of the triangle, it is equidistant from all three sides. Step 3: Let L,…
Why does a circle with centre I and radius IL touch all three sides of the triangle?
Answer
Step 1: I is the incentre, so IL = IM = IN. Step 2: Equal perpendicular distances from the centre to the sides mean the same radius reaches each side. Step 3: A circle drawn with centre I and radius I…
What is the difference between incentre and circumcentre?
Answer
Step 1: The incentre is equidistant from the sides of a triangle. Step 2: The circumcentre is equidistant from the vertices of a triangle. Step 3: The incentre is the intersection of angle bisectors.
In triangle ABC, DP, EQ, and FR are perpendicular bisectors. What do you conclude?
Answer
Step 1: A triangle has three sides, so three perpendicular bisectors can be drawn. Step 2: The three perpendicular bisectors of a triangle are concurrent. Step 3: Their point of concurrency is called …
In triangle ABC, O is the circumcentre. What equality holds for the distances to the vertices?
Answer
Step 1: O lies on the perpendicular bisector of BC, so BO = CO. Step 2: O lies on the perpendicular bisector of AC, so AO = CO. Step 3: Therefore all three distances are equal. Answer: AO = BO = CO.
A circle is drawn with centre O and radius AO. What does this circle do?
Answer
Step 1: O is the circumcentre, so AO = BO = CO. Step 2: A circle with centre O and radius AO passes through A, B, and C. Step 3: A circle passing through all three vertices is the circumcircle. Answer…
Where is the circumcentre of a right triangle located?
Answer
Step 1: The circumcentre changes position with triangle type. Step 2: For a right triangle, it lies on the hypotenuse. Answer: On the hypotenuse.
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