37 Maths -- Geometry: Circle

ABC is an acute-angle triangle. Let P, Q, and R be the feet of the altitude from vertices A, C, and B, respectively, and all three altitudes intersect at O, then prove that ∠𝑂𝑃𝑄 = ∠𝑂𝑃𝑅.

1 Answers

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Let ABC be a acute angled triangle. Let X and Y bé two points on sides AB and Ac respectively such that BXYC is cyclic and AX:BX=1:8. Let XY intersect circumcircle of triangle ABC in P such that Y ...

point M.N.T and S are concyclic such that arc MN = arc CT. if the chord CN and MT are intersectedat a point A . then prove that : 1) area of triangle MAN = area of triangle CAT.2) chord MT = cho...

WXYA is a trapezium. If WZ ∥ XY and M is the mid-point of YZ, then prove that: Area of △ WXM = 1/2 area of trapezium WXYZ.

In a triangle PQR, D, E and F are the midpoints of sides PQ, PR and QR respectively. If G in a point on QR such that PG is perpendicular to QR, then prove that DEFG is a cyclic quadrilateral.

In a cyclic quadrilateral ABCD, CD is produced to E. If AD is the bisector of ∠𝐵𝐷𝐸, prove that △ 𝐴𝐵𝐶 is isosceles.

In the given figure, two circles intersect at P and Q. O is the centre of the smaller circle which lies on the circumference of the larger circle and RO is joined and produced to meet QS at X. Pr...

In triangle PBR, PA = AB and PB is perpendicular to BR. If O is the centre of circle and r is radius then prove that: PQ.PR = 8r2

37 Maths -- Geometry: Circle

ABC is an acute-angle triangle. Let P, Q, and R be the feet of the altitude from vertices A, C, and B, respectively, and all three altitudes intersect at O, then prove that ∠𝑂𝑃𝑄 = ∠𝑂𝑃𝑅.

1 Answers

More questions on Geometry: Circle

Let ABC be a acute angled triangle. Let X and Y bé two points on sides AB and Ac respectively such that BXYC is cyclic and AX:BX=1:8. Let XY intersect circumcircle of triangle ABC in P such that Y ...

point M.N.T and S are concyclic such that arc MN = arc CT. if the chord CN and MT are intersectedat a point A . then prove that : 1) area of triangle MAN = area of triangle CAT.2) chord MT = cho...

WXYA is a trapezium. If WZ ∥ XY and M is the mid-point of YZ, then prove that: Area of △ WXM = 1/2 area of trapezium WXYZ.

In a triangle PQR, D, E and F are the midpoints of sides PQ, PR and QR respectively. If G in a point on QR such that PG is perpendicular to QR, then prove that DEFG is a cyclic quadrilateral.

In a cyclic quadrilateral ABCD, CD is produced to E. If AD is the bisector of ∠𝐵𝐷𝐸, prove that △ 𝐴𝐵𝐶 is isosceles.

In the given figure, two circles intersect at P and Q. O is the centre of the smaller circle which lies on the circumference of the larger circle and RO is joined and produced to meet QS at X. Pr...

In triangle PBR, PA = AB and PB is perpendicular to BR. If O is the centre of circle and r is radius then prove that: PQ.PR = 8r2