1.An isosceles triangle with each leg measuring 13 cm is inscribed in a circle . if the altitude to the base is 12 cm find the radius of the circle

2. Circles a and b are tangent at point c. p is on circle a and q is on circle b such that pq is tangent to both circles. Given ac= 3 cm and bc= 8 cm, find pq

3.Ab is a chord of a circle with center o and radius 52 cm . point m divides the chord ab such that am = 63 cm and mb=33 cm find om

4. A circle is inscribed in a triangle whose sides are 10, 10 and 12 units . a second smaller circle is inscribed tangent to the first circle and to the equal sides of the triangle. Find the radius of the second triangle.


  1. 👍
  2. 👎
  3. 👁
  1. 1. Make a sketch by placing the triangle on the x-y gird so that the altitude falls along the y-axis with (0,12) the top of the triangle and (0,) the middle of the base.
    Look at the righ-angled triangle in the first quadrant.
    You know the hypotenuse is 13 and the height is 12, so by Pythagoras the base must be 5
    So our circle must pass through A(0,12) and B(5,0) and the centre must lie on the y-axis or on x = 0

    You also know that the centre must lie on the right bisector of AB
    Slope of AB = -12/5
    so slope of right bisector is 5/12
    midpoint of AB is (5/2 , 6)
    equation of right-bisector:
    y = (5/12)x + b , with (5/2 , 6) on it, so
    6 = (5/12)(5/2) + b
    b = 6 - 25/24 = 119/24

    so the centre is at P(0 , 119/24)
    and the radius is 12 - 119/24 = 169/24
    or appr 7.04

    2. Please use capital letters for vertices
    I assume the centres of your circles are A and B
    Since the circles are tangents to each other, AB is straight line and AB = 11
    Also you will have right angles at P and Q
    From A draw a line parallel to PQ to hit BQ at D
    APQD will be a rectangle.
    You will have a right-angled triangle and you can find AD, thus PQ

    Give the others a try, I will not be available for the rest of the afternoon

    1. 👍
    2. 👎
  2. equation 2x-3y=10 touches the circle with centre m (-2,4)

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    Can someone please check to see if I answered these true and false statements correctly? Thank you! 1. A triangle can have two right angles. (TRUE??) 2. An equilateral triangle is also an acute. (TRUE??) 3. A right triangle can

  2. Geometry

    An isosceles right triangle has an area of 98cm squared. Find the length of each leg. The formula of finding the area of a triangle with one right angle is: (b x h)/2 You know that an isoceles triangles has two equal sides. Those

  3. Math

    Classify a triangle with angles measuring 69, 42, and 69 my answer is isosceles acute

  4. Geometry

    An isosceles triangle has area of 125 ft2. If the base is 14 ft, what is the length of each leg? Round your answer to the nearest tenth.

  1. Math (Triangles)

    The vertex angle of an isosceles triangle is 40°20'. Each of the leg measures 320 mm. Find the length of the base.


    Which of the statements is ALWAYS TRUE? A-A right triangle is a scalene triangle. B-An equilateral triangle is an isosceles triangle. C-An isosceles triangle is an obtuse triangle. D-A right triangle is an acute triangle. I got

  3. geometry

    An isosceles triangle has two 10.0-inch sides and a 2w-inch side. Find the radius of the inscribed circle of this triangle, in the cases w = 5.00, w = 6.00, and w = 8.00. Then Write an expression for the inscribed radius r in

  4. Math

    Each triangle is a 30-60-90 triangle, and the hypotenuse of one triangle is the longer leg of an adjacent triangle. The hypotenuse of the largest triangle is 8 centimeters. What is the number of centimeters in the length of the

  1. Math

    1) The hypotenuse of an isosceles right triangle is 8 cm longer than either of its legs. Note that an isosceles right triangle is a right triangle whose legs are the same length. Find the exact length of its legs and its


    Which statement is contrapositive of the conditional: If a triangle is isosceles, then it has 2 congruent sides. 1. If a triangle does not have 2 congruent sides, then it is not isosceles. 2. If a triangle is isosceles, then it

  3. math

    Plane A which contains an isosceles right triangle forms a dihedral angle of 60 degrees with another plane B. If the hypotenuse of the triangle lies in plane B and measures 8 in., find the distance from the vertex of the right

  4. geometry

    Each base of an isosceles triangle measures 42 degrees, 30'. The base is 14.6 meters long. a. Find the length of a leg of the triangle b. Find the altitude of the triangle c. What is the area of the triangle?

You can view more similar questions or ask a new question.