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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?
Wiki User
∙ 10y ago
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.
Wiki User
∙ 10y ago
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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
Is the circumcenter of a triangle the center of the circle circumscribed about the triangle?
Yes.
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.
How many circumscribed circles can a triangle have?
A triangle has exactly one circumscribed circle.
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.
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.
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.
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.
