Two concentric circles with center O, seg AB, seg BC are the tangents to the smaller circle at point P, Q and R respectively and also they are chords of the bigger circle. Prove that : Seg PQ is parallel to seg AC, PQ = (1/2)AC. Get link Facebook X Pinterest Email Other Apps September 26, 2018 Read more
If four tangents of a circle determine a rectangle then show that it must be a square. Get link Facebook X Pinterest Email Other Apps September 26, 2018 Read more
In the adjoining figure, AB is a diameter of a circle with center O, Seg AC is a tangent to the circle at point A. Line JD touches circle at point D, and intersects segment AC in point J. Prove that: seg AJ ≅ seg CJ Get link Facebook X Pinterest Email Other Apps September 26, 2018 Read more
In the adjoining figure, line AP is a tangent to a circle with center O at point A. Seg AF is angle bisector of ∠BAC. Prove that: seg AP ≅ seg PE Get link Facebook X Pinterest Email Other Apps September 26, 2018 Read more
The bisectors of the angles A, B of △ABC intersect in I, the bisectors of he corresponding exterior angles intersect in E. Prove that ▢AIBE is cyclic. Get link Facebook X Pinterest Email Other Apps September 26, 2018 Read more
From the end points of a diameter of circle perpendiculars are drawn to a tangent of the same circle. Show that their feet on the tangent are equidistant from the center of circle. Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
Two circles with center O and P intersects each other in point C and D. Chord AB of the circle with center O touches the circle with center P in point E. Prove that: ∠ADE + ∠BCE = 180° Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
Show that the radius of incircle of right angled triangle is equal to the difference of half of the perimeter and the hypotenuse. Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
△ABC is an equilateral triangle. Bisector of Angle B intersects circumcircle of △ABC in point P. Prove that CQ = CA Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
If two circles are internally touching at point P. A line intersect those circles in point A, B, C, D respectively then, Prove that: Angle APB ≅ Angle CPD Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
In the adjoining figure, BC is a diameter of a circle with center M. PA is a tangent at A from P which is a point on line BC. AO perpendicular to BC. PROVE THAT: DP² = BP x CP - BD x CD. Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
In triangleABC, angle A is an obtuse angle. P is the circumcentre of triangleABC. Prove that anglePBC = angleA -90° Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
In the adjoining figure, DE intersects the sides of triangle ABC in point P and Q such that, m(arc AD) = m(arc DB) and m(arc AE) = m(arc EC) SHOW THAT :- Angle PQC ≅ Angle BPQ Get link Facebook X Pinterest Email Other Apps September 25, 2018 Read more
