Home
Class 10
MATHS
In the figure, the radius of a circle wi...

In the figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions.
d(A,B)=6cm, find d(B,C).

Text Solution

Verified by Experts

The correct Answer is:
`d(B,C)= 6sqrt(2)` cm
In `triangle CAB`,
`/_CAB+90^(@)" " "........."[" From (i) "]`
`therefore` by Pythagoras theorem,
`CB^(2)=CA^(2)+AB^(2)`
`therefore BC^(2)=6^(2)+6^(2)`
`therefore BC^(2)= 36+36" " therefore BC^(2)=72`
`:. BC=6sqrt(2) cm " " "......."(" Taking square roots of both the sides ")`
`d(B,C)=BC=6sqrt(2)` cm.
Promotional Banner

Topper's Solved these Questions

  • CIRCLE

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise PRACTICE SET 3.2|8 Videos

  • CIRCLE

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise PRACTICE SET 3.3|3 Videos

  • CIRCLE

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLES FOR PRACTICE|40 Videos

  • CHALLENGING QUESTIONS

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise SECTION 3 (MODEL QUESTION PAPER FOR PRACTICE ) Solve any one of the following subquestions :|1 Videos

  • COORDINATE GEOMETRY

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise Assignment 6.5|13 Videos

Similar Questions

Explore conceptually related problems

In the figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions. What is the measure of /_CAB? Why?.

In the figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A. Answer the following questions. What is the distance of point C from line AB? Why?

In the figure, the radius of a circle with centre C is 6 cm, line AB is a tangent at A and AB is 6 cm. Answer the following questions. What is the measure of /_ABC? Why?.

In the adjoining figure, the radius of a circle with centre C is 6cm , line AB is a tangent at A. Answer the following question (i) What is the measure of angle CAB ? Why? (ii) What is the distance of point C from line AB? Why? (iii) d(A,B)=6cm, find d(B,C). (iv) What is the measure of angleABC ? Why?

In the figure RQ is a tangent to the circle with centre O. If SQ=6cm, QR=4cm, find OR.

In the adjoining figure, AB is a chord of length 9.6 cm of a circle with centre O and radius 6 cm. The tangents at A and B intersect at P. Find the length of PA.

In the figure, point P is the centre of the circle and line AB is the tangent to the circle at the point T. The radius of the circle is 6 cm . Find PB, if /_ TPB = 60^(@)

In a triangle ABC if sides AB = c = 4 cm, side AC = b = 6 cm and BC = a = 7, then answer the following questions The length of median AD is

Find the length of the tangent to a circle with centre O and radius 6cm from a point P such that OP=10cm?

In the given figure , (i) the radii of the circles with centres A and B are 3cm and 4cm respectively. (ii) the radii of the circles with centres A and B are 4cm and 3cm respectively. Find (i) d(A,B) in figure (a) (ii) d(A,B) in figure (b)