Question
In the given figure P is the incenter, find PD
- 4
- 6
- 9
- 15
Hint:
Indirectly, they have asked to find the radius of the incircle. Then, apply Pythagorean theorem to a triangle where we can obtain the radius of the incircle.
The correct answer is: 6
Given That:
>>Here P is an incenter and the radius is PE = PD = PF.
>>Now from the triangle BPE,
We apply Pythagorean theorem,
PE = 6 units.
>>>Therefore, the measure of PE is 6 units.
To obtain the radius of the incircle, we know that the points D, E, F are the perpendicular bisector points. Hence, the angle must be 90 degrees. We can now apply Pythagorean theorem to obtain the unknown values.
Related Questions to study
If a circle is drawn through the point of concurrency of given figure, find the radius of the circle.
The points of concurrency are D, E, F then P becomes the center of the circle and that circle generally called as a incircle of a triangle. Radius of incircle can be found easily applying the Pythagorean theorem to any one of the triangle.
>>>>
>>>PE = 3 units.
If a circle is drawn through the point of concurrency of given figure, find the radius of the circle.
The points of concurrency are D, E, F then P becomes the center of the circle and that circle generally called as a incircle of a triangle. Radius of incircle can be found easily applying the Pythagorean theorem to any one of the triangle.
>>>>
>>>PE = 3 units.
Find MP in the given figure.
Always angular bisector divides the given angle into 2 equal parts. Then, by equalizing the the two equations we can get the measure of angles easily.
Find MP in the given figure.
Always angular bisector divides the given angle into 2 equal parts. Then, by equalizing the the two equations we can get the measure of angles easily.
Find ∠DAC in the given figure.
For such questions, we should know the properties of the angle bisector.
Find ∠DAC in the given figure.
For such questions, we should know the properties of the angle bisector.
Identify the theorem used to solve the problem.
Identify the theorem used to solve the problem.
In a scalene triangle, the incenter lies ____.
In a scalene triangle, the incenter lies ____.
If P is equidistant from all the sides of the triangle ABC, then a circle drawn with P as the center touching all the sides, then the center of the circle is also called ______.
For such questions, we should know about the different centers of the circle and triangle.
If P is equidistant from all the sides of the triangle ABC, then a circle drawn with P as the center touching all the sides, then the center of the circle is also called ______.
For such questions, we should know about the different centers of the circle and triangle.
From the given figure,
Find the relation between P and ∠NOM.
From the given figure,
Find the relation between P and ∠NOM.
From the given figure, if BD ⊥ AB, DC ⊥ AC, then find the relation between BD and DC.
From the given figure, if BD ⊥ AB, DC ⊥ AC, then find the relation between BD and DC.
Direction : Among given options only for this figure perpendicular bisector theorem is used.
If AD = 8 units, find BD.
the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle.
Direction : Among given options only for this figure perpendicular bisector theorem is used.
If AD = 8 units, find BD.
the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle.
Direction : Among given options only for this figure perpendicular bisector theorem is used.
If BD = 5 units, find AD.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. T
Direction : Among given options only for this figure perpendicular bisector theorem is used.
If BD = 5 units, find AD.
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. T
Find length of perpendicular bisector of CB
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. T
Find length of perpendicular bisector of CB
Pythagoras theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. T
Which of the following triangles have the same side lengths?
Which of the following triangles have the same side lengths?
