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Triangle pqr is an isosceles triangle in which pq equals pr equals 5cm it is circumscribed about a circle prove that qr is bisected at point of contact?
Suppose the circle meets QR at A, RP at B and PQ at C.
PQ = PR (given)
so PC + CQ = PB + BR.
But PC and PB are tangents to the circle from point P, so PC = PB.
Therefore CQ = BR
Now CQ and AQ are tangents to the circle from point Q, so CQ = AQ
and BR and AR are tangents to the circle from point R, so BR = AR
Therefore AQ = AR, that is, A is the midpoint of QR.
What else can I help you with?
The center of the circumscribed circle lies on line segment and the longest side of the triangle is equal to the o?
If the center of the circumscribed circle (circumcenter) lies on a line segment of the triangle, it indicates that the triangle is isosceles or degenerate. In an isosceles triangle, the circumcenter lies along the line segment connecting the apex to the midpoint of the base. If the longest side of the triangle is equal to the circumradius, it suggests a specific relationship between the triangle's dimensions and its circumcircle. This scenario can occur in certain configurations, but further clarification is needed for a complete analysis.
Are isosceles triangle sometimes an equilateral triangle?
Are isosceles triangle sometimes an equilateral triangle
Are the sides of a circumscribed equilateral triangle bisected at the points of contact to the circle?
Yes. One can satisfy oneself that this is true just by considering the symmetry of the construction.
Is the incenter of a triangle the center of the circle circumscribed about the triangle?
No.
What is an example of an isosceles triangle?
isosceles triangle
Define a circumscribed triangle?
a circumscribed triangle is a circumscribed triangle and will always be
How unusual is the square shape?
No more unusual than the right isosceles triangle, which is a diagonally-bisected square.
Can the angle bisector of a triangle also be the perpendicular bisector?
Yes. The bisector of one angle of a triangle is the perpendicular bisector of theopposite side if the bisected angle is the vertex angle of an isosceles triangle,or any angle of an equilateral triangle.
How many circumscribed circles can a triangle have?
A triangle has exactly one circumscribed circle.
Does the angle bisector of the vertex angle of an isosceles triangle divides the triangle into two congruent?
Only if the vertex angle being bisected is between the sides of equal length will the result be two congruent triangles.
Is an acute triangle sometimes an isosceles?
An acute triangle can be an isosceles triangle, but it doesn't have to be. An isosceles triangle can be an acute triangle, but it doesn't have to be.
The center of the circumscribed circle lies on line segment and the longest side of the triangle is equal to the o?
If the center of the circumscribed circle (circumcenter) lies on a line segment of the triangle, it indicates that the triangle is isosceles or degenerate. In an isosceles triangle, the circumcenter lies along the line segment connecting the apex to the midpoint of the base. If the longest side of the triangle is equal to the circumradius, it suggests a specific relationship between the triangle's dimensions and its circumcircle. This scenario can occur in certain configurations, but further clarification is needed for a complete analysis.
What does a right triangle and an isosceles triangle have in common?
A right triangle and an isosceles triangle have the fact that they are both triangles in common. A right triangle can also be an isosceles triangle.
To circumscribed a circle about a triangle you use the?
To circumscribed a circle about a triangle you use the angle. This is to get the right measurements.
Ans isosceles triangle is a triangle that has?
An isosceles triangle is a triangle that has two equal sides.
Are isosceles triangle sometimes an equilateral triangle?
Are isosceles triangle sometimes an equilateral triangle
Is the incenter of a triangle the center of the circle circumscribed about the triangle?
No.
