Advertisements
Advertisements
Question
In the following figure, XY = 10 cm and LT = 4 cm. Find the length of XT.
Advertisements
Solution
Given: XY = 10 cm and LT = 4 cm
Congruent tangent segments are those drawn from an exterior point to a circle.
Thus, XY = XZ = 10 cm
Similarly, LT = TZ = 4 cm
Now, XT = XZ – TZ
= 10 – 4
= 6 cm
Hence, the length of XT is 6 cm.
APPEARS IN
RELATED QUESTIONS
In the adjoining figure, O is the centre of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then
- What is the length of each tangent segment?
- What is the measure of ∠MRO?
- What is the measure of ∠MRN?
Seg RM and seg RN are tangent segments of a circle with centre O. Prove that seg OR bisects ∠MRN as well as ∠MON with the help of activity.
In the given figure, the circles with centres A and B touch each other at E. Line l is a common tangent which touches the circles at C and D respectively. Find the length of seg CD if the radii of the circles are 4 cm, 6 cm. 
In the given figure, seg EF is a diameter and seg DF is a tangent segment. The radius of the circle is r. Prove that, DE × GE = 4r2
Four alternative answers for the following question is given. Choose the correct alternative.
Length of a tangent segment drawn from a point which is at a distance 12.5 cm from the centre of a circle is 12 cm, find the diameter of the circle.
In the given figure, M is the centre of the circle and seg KL is a tangent segment.
If MK = 12, KL = \[6\sqrt{3}\] then find –
(1) Radius of the circle.
(2) Measures of ∠K and ∠M.
In the given figure, M is the centre of the circle and seg KL is a tangent segment. L is a point of contact. If MK = 12, KL = `6sqrt3`, then find the radius of the circle.
Prove the following theorem:
Tangent segments drawn from an external point to the circle are congruent.
Segment DP and segment DQ are tangent segments to the circle with center A. If DP = 7 cm. So find the length of the segment DQ?
The chords corresponding to congruent arcs of a circle are congruent. Prove the theorem by completing following activity.
Given: In a circle with centre B
arc APC ≅ arc DQE
To Prove: Chord AC ≅ chord DE
Proof: In ΔABC and ΔDBE,
side AB ≅ side DB ...`square`
side BC ≅ side `square` ...`square`
∠ABC ≅ ∠DBE ...[Measure of congruent arcs]
∆ABC ≅ ∆DBE ...`square`
Length of a tangent segment drawn from a point which is at a distance 15 cm from the centre of a circle is 12 cm, find the diameter of the circle?
In the adjoining figure, O is the center of the circle. From point R, seg RM and seg RN are tangent segments touching the circle at M and N. If (OR) = 10 cm and radius of the circle = 5 cm, then
- What is the length of each tangent segment?
- What is the measure of ∠MRO?
- What is the measure of ∠MRN?
If AB and CD are the common tangents in the circles of two unequal (different) radii, then show that seg AB ≅ seg CD.
Prove that, tangent segments drawn from an external point to the circle are congruent.
In a parallelogram ABCD, ∠B = 105°. Determine the measure of ∠A and ∠D.
