Advertisements
Advertisements
प्रश्न
In the adjoining figure, the line MN touches the circle with center A at point M. If AN = 13 and MN = 5, then find the radius of the circle?
उत्तर
In given figure, AM is the radius of the circle.
In ∆AMN,
∠AMN = 90° ......[Tangent theorem]
∴ AN2 = AM2 + MN2 ......[Pythagoras theorem]
∴ 132 = AM2 + 52 ......[Given]
∴ 169 = AM2 + 25
∴ AM2 = 169 – 25
∴ AM2 = 144
∴ AM = 12 ......[Taking square root of both sides]
∴ The radius of the circle is 12 units.
APPEARS IN
संबंधित प्रश्न
P is the centre of the circle and its radius is
10 cm. Distance of a chord AB from the centre is 6 cm. Find the length of chord AB.
Radius of circular base of an ear of corn is 6.6 cm and its length is
11.2 cm. If on an average 1 sqcm area contains 2 corn kernels, find the
total number of kernels on a corn.
Side of square ABCD is 7 cm. With D as the centre and DA as radius, arc AXC is drawn.Find the area of the shaded region with the help of the following flow chart .
There is a hemispherical bowl. A cone is to be made such that, if it is filled with water twice and the water is poured in the bowl, it will be filled just completely. State how will you decide the radius and perpendicular height of the cone.
In the figure, line l touches the circle with center O at point P. Q is the midpoint of radius OP. RS is a chord through Q such that chords RS || line l. If RS = 12, find the radius of the circle.
Draw the tangent at any point M on the circle with centre O and radius 2.9 cm.
Draw a tangent at any point ‘M’ on the circle of radius 3.3 cm and centre ‘O’.
In the adjoining figure the radius of a circle with centre C is 6 cm, line AB is a tangent at A. What is the measure of ∠CAB? Why?
In the adjoining figure, circle with center D touches the sides of ∠ACB at A and B. If ∠ACB = 52°, find measure of ∠ADB.
AP is a tangent at A drawn to the circle with centre O from an external point P. OP = 12 cm and ∠OPA = 30°, then the radius of a circle is ______.
Draw a circle with centre O having radius 3 cm. Draw tangent segments PA and PB through the point P outside the circle such that ∠APB = 70°.
