Chapter 10 – Circles
12. AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre, prove that 4q^2 = p^2 + 3r^2.
02
Jul
12. AB and AC are two chords of a circle of radius r such that AB = 2AC. If p and q are the distances of AB and AC from the centre, prove that 4q^2 = p^2 + 3r^2. 12. AB and AC are two chords of a circle of radius r such that AB [...]
11. Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB = PD.
02
Jul
11. Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB = PD. 11. Two equal chords AB and CD of a circle when produced intersect at a point P. Prove that PB = PD. July 2, 2021 Category: Chapter 10 - Circles , Maths , [...]
10. A circle has radius root 2 cm. It is divided into two segments by a chord of length 2 cm. Prove that the angle subtended by the chord at a point in major segment is 45º.
02
Jul
10. A circle has radius root 2 cm. It is divided into two segments by a chord of length 2 cm. Prove that the angle subtended by the chord at a point in major segment is 45º. 10. A circle has radius root 2 cm. It is divided into two segments by a chord of [...]
9. If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, prove that PQ is a diameter of the circle.
02
Jul
9. If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle, circumscribing it at the points P and Q, prove that PQ is a diameter of the circle. 9. If bisectors of opposite angles of a cyclic quadrilateral ABCD intersect the circle circumscribing it at the points P and Q prove that [...]
8. In Fig. 10.19, AB and CD are two chords of a circle intersecting each other at point E. Prove that ∠AEC = 1/2 (Angle subtended by arc CXA at centre + angle subtended by arc DYB at the centre).
02
Jul
8. In Fig. 10.19, AB and CD are two chords of a circle intersecting each other at point E. Prove that ∠AEC = 1/2 (Angle subtended by arc CXA at centre + angle subtended by arc DYB at the centre). 8. In Fig. 10.19 AB and CD are two chords of a circle intersecting each [...]
7. If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠BPC.
02
Jul
7. If ABC is an equilateral triangle inscribed in a circle and P be any point on the minor arc BC which does not coincide with B or C, prove that PA is angle bisector of ∠BPC. 7. If ABC is an equilateral triangle inscribed in a circle and P be any point on the [...]
6. If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see Fig.10.18), prove that arc CXA + arc DZB = arc AYD + arc BWC = semicircle.
02
Jul
6. If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see Fig.10.18), prove that arc CXA + arc DZB = arc AYD + arc BWC = semicircle. 6. If two chords AB and CD of a circle AYDZBWCX intersect at right angles (see Fig.10.18) prove that arc CXA + arc [...]
5. Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle
02
Jul
5. Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect, they will intersect on the circumcircle of the triangle 5. Prove that angle bisector of any angle of a triangle and perpendicular bisector of the opposite side if intersect they will intersect on the circumcircle [...]
4. ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic.
02
Jul
4. ABCD is a parallelogram. A circle through A, B is so drawn that it intersects AD at P and BC at Q. Prove that P, Q, C and D are concyclic. -q 4. ABCD is a parallelogram. A circle through A B is so drawn that it intersects AD at P and BC at [...]
3. If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic.
02
Jul
3. If P, Q and R are the mid-points of the sides BC, CA and AB of a triangle and AD is the perpendicular from A on BC, prove that P, Q, R and D are concyclic. -q 3. If P CA and AB of a triangle and AD is the perpendicular from A on [...]