37 Maths -- Geometry: Circle

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. Prove that RQ = RS.

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 ...

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37 Maths -- Geometry: Circle

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. Prove that RQ = RS.

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 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

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.