Here we will solve different types of Problems on properties of tangents.

**1.** A tangent, PQ, to a circle touches it at Y. XY is a chord
such that ∠XYQ = 65°. Find ∠XOY, where O is the centre of the circle.

**Solution:**

Let Z be any point on the circumference in the segment alternate ∠XYQ.

Therefore, ∠XZY = ∠XYQ = 65°, as the angle between a chord and a tangent is equal to the angle in the alternate segment.

∠XOY = 2∠XZY, as angle at the centre is double the angle at the circumference.

Therefore, ∠XOY = 2 × 65° = 130°.

**2.** XY is a chord of a given circle, which on producing, meets
the tangent TZ at Z. If XY = 5 cm and YZ = 4 cm, find TZ.

**Solution:**

XZ = XY + YZ

= 5 cm + 4 cm

= 9 cm.

Again, we know that

XZ × YZ = TZ^2

⟹ 9 cm × 4 cm = TZ^2

⟹ 36 cm^2 = TZ^2

⟹ TZ = \(\sqrt{36 cm^2}\)

⟹ TZ = 6 cm.

**From ****Problems on Properties of Tangents**** to HOME PAGE**

**Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.**

## New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.