Tangents and Intersecting Chords Mathematics - Tangents and Intersecting Chords

In the following figure, PQ is the tangent to the circle at A, DB is the diameter and O is the centre of the circle. If ∠ADB = 30° and ∠CBD = 60°, Calculate: ∠QAB 

In the following figure, PQ is the tangent to the circle at A, DB is a diameter and O is the centre of the circle. If ∠ ADB = 30° and ∠ CBD = 60° ; calculate : ∠CDB

In the following figure, PQ is the tangent to the circle at A, DB is a diameter and O is the centre of the circle. If ∠ ADB = 30° and ∠ CBD = 60° ; calculate ∠ PAD.

In the given figure, C and D are points on the semi-circle described on AB as diameter. Given angle BAD = 70° and angle DBC = 30°, calculate angle BDC.

The diameter and a chord of a circle have a common end-point. If the length of the diameter is 20 cm and the length of the chord is 12 cm, how far is the chord from the centre of the circle?

In the given figure, AE and BC intersect each other as point D.

If ∠CDE = 90°, AB = 5cm, BD = 4cm and CD = 9 cm find AE.

In the given figure, O is the centre of the circle. The tangents at B and D intersect each other at point P. If AB is parallel to CD and ∠ABC = 55°, find:

(i) ∠BOD (ii) ∠BPD

In the given figure, AB is the diameter. The tangent at C meets AB produced at Q.
If ∠CAB = 34°, Find : ∠CBA

AB is a line segment and M is its mid – point three semi circles are drawn with AM, MB and AB as diameter on the same side of the line AB. A circle with radius r unit is drawn so  that it  touches all the three semi circles show that : AB = 6 × r

The given figure shows a semi-circle with centre O and diameter PQ. If PA = AB and ∠BCQ =140°; Find measures of angles PAB and AQB. Also, show that AO is parallel to BQ.

In a square ABCD, its diagonals AC and BD intersect each other at point O. the bisector of angle DAO meets BD at point M and the bisector of angle ABD meets AC at N and AM at L. Show that:
∠ ONL + ∠ OML = 180

ABC is a triangle with AB = 10 cm, BC = 8 cm and AC = 6 cm (not drawn to scale). Three circle are drawn touching each other with the vertices as their centres. Find the radii of the three circles

Prove that, of any two chords of a circle, the greater chord is nearer to the centre.

Show that the circle drawn on any one of the equal sides of an isosceles triangle as diameter bisects the base.

In cyclic quadrilateral ABCD, ∠A = 3 ∠C and ∠D = 5 ∠B. Find the measure of each angle of the quadrilateral.

ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = 110° and angle BAC = 50°. Find angle DAC and angle DCA.

Two chords AB and AC of a circle are equal. Prove that the centre of the circle lies on the bisector of angle BAC.

In the figure given below, O is the center of the circle of the circle and SP is a tangent. if ∠SRT=65°, find the value of x, y and Z.